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Journal articles on the topic 'Strichartz inequalities'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Bennett, Jonathan, Neal Bez, and Marina Iliopoulou. "Flow Monotonicity and Strichartz Inequalities." International Mathematics Research Notices 2015, no. 19 (2014): 9415–37. http://dx.doi.org/10.1093/imrn/rnu230.

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2

Adekoya, Oreoluwa, and John P. Albert. "Maximisers for Strichartz inequalities on the torus." Nonlinearity 35, no. 1 (2021): 311–42. http://dx.doi.org/10.1088/1361-6544/ac37f4.

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Abstract We study the existence of maximisers for a one-parameter family of Strichartz inequalities on the torus. In general, maximising sequences can fail to be precompact in L 2 ( T ) , and maximisers can fail to exist. We provide a sufficient condition for precompactness of maximising sequences (after translation in Fourier space), and verify the existence of maximisers for a range of values of the parameter. Maximisers for the Strichartz inequalities correspond to stable, periodic (in space and time) solutions of a model equation for optical pulses in a dispersion-managed fiber.

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3

Bouclet, Jean-Marc. "Strichartz Inequalities on Surfaces with Cusps." International Mathematics Research Notices 2015, no. 24 (2015): 13437–92. http://dx.doi.org/10.1093/imrn/rnv105.

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4

Fanelli, Luca, Luis Vega, and Nicola Visciglia. "Existence of maximizers for Sobolev–Strichartz inequalities." Advances in Mathematics 229, no. 3 (2012): 1912–23. http://dx.doi.org/10.1016/j.aim.2011.12.012.

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5

Ginibre, J., and G. Velo. "Generalized Strichartz Inequalities for the Wave Equation." Journal of Functional Analysis 133, no. 1 (1995): 50–68. http://dx.doi.org/10.1006/jfan.1995.1119.

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6

Han, Wei. "The sharp Strichartz and Sobolev-Strichartz inequalities for the fourth-order Schrödinger equation." Mathematical Methods in the Applied Sciences 38, no. 8 (2014): 1506–14. http://dx.doi.org/10.1002/mma.3164.

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7

Barceló, J. A., J. M. Bennett, A. Carbery, A. Ruiz, and M. C. Vilela. "Strichartz inequalities with weights in Morrey-Campanato classes." Collectanea mathematica 61, no. 1 (2010): 49–56. http://dx.doi.org/10.1007/bf03191225.

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8

Fanelli, Luca, and Luis Vega. "Magnetic virial identities, weak dispersion and Strichartz inequalities." Mathematische Annalen 344, no. 2 (2008): 249–78. http://dx.doi.org/10.1007/s00208-008-0303-7.

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9

Mejjaoli, Hatem. "Generalized Lorentz Spaces and Applications." Journal of Function Spaces and Applications 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/302941.

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We define and study the Lorentz spaces associated with the Dunkl operators onℝd. Furthermore, we obtain the Strichartz estimates for the Dunkl-Schrödinger equations under the generalized Lorentz norms. The Sobolev inequalities between the homogeneous Dunkl-Besov spaces and generalized Lorentz spaces are also considered.

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10

Fanelli, Luca, and Nicola Visciglia. "The lack of compactness in the Sobolev–Strichartz inequalities." Journal de Mathématiques Pures et Appliquées 99, no. 3 (2013): 309–20. http://dx.doi.org/10.1016/j.matpur.2012.06.015.

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11

Mouzard, Antoine, and Immanuel Zachhuber. "Strichartz inequalities with white noise potential on compact surfaces." Analysis & PDE 17, no. 2 (2024): 421–54. http://dx.doi.org/10.2140/apde.2024.17.421.

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12

Brocchi, Gianmarco, Diogo Oliveira e Silva, and René Quilodrán. "Sharp Strichartz inequalities for fractional and higher-order Schrödinger equations." Analysis & PDE 13, no. 2 (2020): 477–526. http://dx.doi.org/10.2140/apde.2020.13.477.

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13

Burq, Nicolas, P. Gerard, and N. Tzvetkov. "Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds." American Journal of Mathematics 126, no. 3 (2004): 569–605. http://dx.doi.org/10.1353/ajm.2004.0016.

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14

Banica, Valeria. "Dispersion and Strichartz Inequalities for Schrödinger Equations with Singular Coefficients." SIAM Journal on Mathematical Analysis 35, no. 4 (2003): 868–83. http://dx.doi.org/10.1137/s0036141002415025.

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15

on Kim, Seongy, Ihy ok Seo, and Jihy on Seok. "Note on Strichartz inequalities for the wave equation with potential." Mathematical Inequalities & Applications, no. 1 (2020): 377–82. http://dx.doi.org/10.7153/mia-2020-23-29.

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16

CAZENAVE, THIERRY, LUIS VEGA, and MARI CRUZ VILELA. "A NOTE ON THE NONLINEAR SCHRÖDINGER EQUATION IN WEAK LpSPACES." Communications in Contemporary Mathematics 03, no. 01 (2001): 153–62. http://dx.doi.org/10.1142/s0219199701000317.

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We study the global Cauchy problem for the equation iut+Δu+λ|u|αu=0 in ℝN. Using generalized Strichartz' inequalities we show that, under some restrictions on α, if the initial value is sufficiently small in some weak Lpspace then there exists a global solution. This result provides a common framework to the "classical" Hssolutions and to the self-similar solutions, thereby extending previous results by Planchon.

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17

Castella, F. "L2 Solutions to the Schrödinger–Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects." Mathematical Models and Methods in Applied Sciences 07, no. 08 (1997): 1051–83. http://dx.doi.org/10.1142/s0218202597000530.

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We study a system of infinitely many coupled Schrödinger equations with self-consistent Coulomb potential as the initial data has only a regularity of L2-type. We first establish Strichartz' inequalities in the framework of vector-valued wave functions (density matrices). This allows us to prove a well-posedness result, and strong smoothing effects. Also, we state blow-up (resp. decay) estimates for the solution as time goes to zero (resp. infinity).

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18

Frank, Rupert L., and Julien Sabin. "Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates." American Journal of Mathematics 139, no. 6 (2017): 1649–91. http://dx.doi.org/10.1353/ajm.2017.0041.

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19

Furioli, Giulia, Camillo Melzi, and Alessandro Veneruso. "Strichartz Inequalities for the Wave Equation with the Full Laplacian on the Heisenberg Group." Canadian Journal of Mathematics 59, no. 6 (2007): 1301–22. http://dx.doi.org/10.4153/cjm-2007-056-1.

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AbstractWe prove dispersive and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on the Heisenberg group, by means of Besov spaces defined by a Littlewood–Paley decomposition related to the spectral resolution of the full Laplacian. This requires a careful analysis due also to the non-homogeneous nature of the full Laplacian. This result has to be compared to a previous one by Bahouri, Gérard and Xu concerning the solution of the wave equation related to the Kohn Laplacian.

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20

Liu, Heping, and Manli Song. "Strichartz Inequalities for the Wave Equation with the Full Laplacian on H-Type Groups." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/219375.

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We generalize the dispersive estimates and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on H-type groups, by means of Besov spaces defined by a Littlewood-Paley decomposition related to the spectral of the full Laplacian. The dimension of the center on those groups ispand we assume thatp>1. A key point consists in estimating the decay in time of theL∞norm of the free solution. This requires a careful analysis due also to the nonhomogeneous nature of the full Laplacian.

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21

Roy, Tristan. "On Jensen-type Inequalities for Nonsmooth Radial Scattering Solutions of a Loglog Energy-Supercritical Schrödinger Equation." International Mathematics Research Notices 2020, no. 8 (2018): 2501–41. http://dx.doi.org/10.1093/imrn/rny045.

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Abstract We prove scattering of solutions of the loglog energy-supercritical Schrödinger equation $i \partial _{t} u + \triangle u = |u|^{\frac{4}{n-2}} u g(|u|)$ with $g(|u|) := \log ^{\gamma } {( \log{(10+|u|^{2})} )}$, $0 &lt; \gamma &lt; \gamma _{n}$, n ∈ {3, 4, 5}, and with radial data $u(0) := u_{0} \in \tilde{H}^{k}:= \dot{H}^{k} (\mathbb{R}^{n})\,\cap\,\dot{H}^{1} (\mathbb{R}^{n})$, where $\frac{n}{2} \geq k&gt; 1 \left(\text{resp.}\,\frac{4}{3}&gt; k &gt; 1\right)$ if n ∈ {3, 4} (resp. n = 5). The proof uses concentration techniques (see e.g., [ 2, 12]) to prove a

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22

BACHELOT, ALAIN. "WAVE PROPAGATION AND SCATTERING FOR THE RS2 BRANE COSMOLOGY MODEL." Journal of Hyperbolic Differential Equations 06, no. 04 (2009): 809–61. http://dx.doi.org/10.1142/s0219891609002003.

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We study the wave equation for the gravitational fluctuations in the Randall–Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some L1-L∞, L2-L∞ decay estimates and global Lp Strichartz type inequalities. We develop the complete scattering theory: existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the

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23

Ivanovici, Oana. "Counterexamples to the Strichartz inequalities for the wave equation in general boundary domains." Journal of the European Mathematical Society 14, no. 5 (2012): 1357–88. http://dx.doi.org/10.4171/jems/335.

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24

Anton, Ramona. "Strichartz inequalities for Lipschitz metrics on manifolds and nonlinear Schrödinger equation on domains." Bulletin de la Société mathématique de France 136, no. 1 (2008): 27–65. http://dx.doi.org/10.24033/bsmf.2548.

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25

Bournaveas, Nikolaos, and Benoit Perthame. "Averages over spheres for kinetic transport equations; hyperbolic Sobolev spaces and Strichartz inequalities." Journal de Mathématiques Pures et Appliquées 80, no. 5 (2001): 517–34. http://dx.doi.org/10.1016/s0021-7824(00)01191-0.

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26

Furioli, Giulia, and Alessandro Veneruso. "Strichartz inequalities for the Schrödinger equation with the full Laplacian on the Heisenberg group." Studia Mathematica 160, no. 2 (2004): 157–78. http://dx.doi.org/10.4064/sm160-2-4.

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27

Hidano, Kunio, and Yuki Kurokawa. "Weighted HLS inequalities for radial functions and Strichartz estimates for wave and Schrödinger equations." Illinois Journal of Mathematics 52, no. 2 (2008): 365–88. http://dx.doi.org/10.1215/ijm/1248355340.

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28

Zhao, Xiaoli. "Research on p order nonlinear half wave Schrödinger equations." Transactions on Environment, Energy and Earth Sciences 1 (March 19, 2024): 103–13. http://dx.doi.org/10.62051/cbbwpx39.

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The objective of our research is to scrutinize the presence and singularity of the comprehensive potent solution for the half-wave Schrödinger equation characterized by order. Take into account the nonlinear half-wave Schrödinger equations represented by order: . We apply the Brezis-Gallouet style inequality to attain a logarithmic form of regulation. These rationales will be pivotal in validating our primary theorem within Global Well-Posedness. When discussing global Solutions, we infer the solutions for Schrödinger equations within the realm when . Specifically, when , we leverage the Stric

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29

QIU, HUA. "Exact Hausdorff and packing measures of Cantor sets with overlaps." Ergodic Theory and Dynamical Systems 35, no. 8 (2014): 2632–68. http://dx.doi.org/10.1017/etds.2014.48.

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Let $K$ be the attractor of a linear iterated function system (IFS) $S_{j}(x)={\it\rho}_{j}x+b_{j},j=1,\ldots ,m$, on the real line $\mathbb{R}$ satisfying the generalized finite type condition (whose invariant open set ${\mathcal{O}}$ is an interval) with an irreducible weighted incidence matrix. This condition was recently introduced by Lau and Ngai [A generalized finite type condition for iterated function systems. Adv. Math.208 (2007), 647–671] as a natural generalization of the open set condition, allowing us to include many important overlapping cases. They showed that the Hausdorff and

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30

Di, Boning, and Dunyan Yan. "Extremals for $$\alpha $$-Strichartz Inequalities." Journal of Geometric Analysis 33, no. 4 (2023). http://dx.doi.org/10.1007/s12220-022-01185-7.

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31

Hundertmark, D., and V. Zharnitsky. "On sharp Strichartz inequalities in low dimensions." International Mathematics Research Notices, January 1, 2006. http://dx.doi.org/10.1155/imrn/2006/34080.

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32

Bulut, Aynur. "Maximizers for the Strichartz Inequalities for the wave equation." Differential and Integral Equations 23, no. 11/12 (2010). http://dx.doi.org/10.57262/die/1356019072.

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33

Goldberg, M., L. Vega, and N. Visciglia. "Counterexamples of Strichartz inequalities for Schrodinger equations with repulsive potentials." International Mathematics Research Notices, January 1, 2006. http://dx.doi.org/10.1155/imrn/2006/13927.

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34

Wang, Haoran. "Strichartz estimates for the Schrödinger and wave equations with a Laguerre potential on the plane." Mathematische Nachrichten, February 17, 2025. https://doi.org/10.1002/mana.202400168.

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AbstractIn this paper, we obtain a set of Strichartz inequalities for solutions to the Schrödinger and wave equations with a Laguerre potential on the plane. To obtain the desired inequalities, we intend to prove the dispersive estimates for the involved Schrödinger and wave propagators and then a standard argument will enable us to arrive at these inequalities. The proof of the dispersive estimate for the Schödinger propagator relies on a crucial uniform boundedness of a series involving the Bessel functions of the first kind, while the dispersive estimate for the wave equation follows from a

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35

Oliveira e Silva, Diogo. "The endpoint Stein–Tomas inequality: old and new." São Paulo Journal of Mathematical Sciences, April 22, 2024. http://dx.doi.org/10.1007/s40863-024-00422-x.

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AbstractThe Stein–Tomas inequality from 1975 is a cornerstone of Fourier restriction theory. Despite its respectable age, it is a fertile ground for current research. This note is centered around three classical applications – to Strichartz inequalities, Salem sets and Roth’s theorem in the primes – and three recent improvements: the sharp endpoint Stein–Tomas inequality in three space dimensions, maximal and variational refinements, and the symmetric Stein–Tomas inequality with applications.

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36

BOUCLET, Jean-Marc, and Haruya MIZUTANI. "Global in time Strichartz inequalities on asymptotically flat manifolds with temperate trapping." Mémoires de la Société mathématique de France, September 18, 2024. http://dx.doi.org/10.24033/msmf.490.

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37

Feng, Guoxia, and Manli Song. "Restriction Theorems and Strichartz Inequalities for the Laguerre Operator Involving Orthonormal Functions." Journal of Geometric Analysis 34, no. 9 (2024). http://dx.doi.org/10.1007/s12220-024-01740-4.

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38

Senapati, P. Jitendra Kumar, Pradeep Boggarapu, Shyam Swarup Mondal, and Hatem Mejjaoli. "Restriction Theorem for the Fourier–Dunkl Transform and Its Applications to Strichartz Inequalities." Journal of Geometric Analysis 34, no. 3 (2024). http://dx.doi.org/10.1007/s12220-023-01530-4.

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39

Mondal, Shyam Swarup, and Manli Song. "Orthonormal Strichartz inequalities for the (k, a)-generalized Laguerre operator and Dunkl operator." Israel Journal of Mathematics, May 9, 2025. https://doi.org/10.1007/s11856-025-2762-x.

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40

Farah, Luiz G., and Henrique Versieux. "On the lack of compactness and existence of maximizers for some Airy-Strichartz inequalities." Differential and Integral Equations 31, no. 1/2 (2018). http://dx.doi.org/10.57262/die/1509041400.

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41

Furioli, Giulia, and Alessandro Veneruso. "Strichartz inequalities for the Schrödinger equation with the full Laplacian on the Heisenberg group." November 26, 2008. https://doi.org/10.4064/sm160-2-4.

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42

Saanouni, Tarek, Salah Boulaaras, and Congming Peng. "A note on inhomogeneous fractional Schrödinger equations." Boundary Value Problems 2023, no. 1 (2023). http://dx.doi.org/10.1186/s13661-023-01721-6.

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AbstractWe study some energy well-posedness issues of the Schrödinger equation with an inhomogeneous mixed nonlinearity and radial data $$ i\dot{u}-(-\Delta )^{s} u \pm \vert x \vert ^{\rho} \vert u \vert ^{p-1}u\pm \vert u \vert ^{q-1}u=0, \quad 0< s< 1, \rho \neq 0, p,q>1. $$ i u ˙ − ( − Δ ) s u ± | x | ρ | u | p − 1 u ± | u | q − 1 u = 0 , 0 < s < 1 , ρ ≠ 0 , p , q > 1 . Our aim is to treat the competition between the homogeneous term $|u|^{q-1}u$ | u | q − 1 u and the inhomogeneous one $|x|^{\rho}|u|^{p-1}u$ | x | ρ | u | p − 1 u . We simultaneously treat two different re

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43

Emmerson, Parker Yaohushuason. "Geometry of Phenomenological Velocity: Energy Numbers, Curvature and Fukaya-Type Categories." May 27, 2025. https://doi.org/10.5281/zenodo.15523017.

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Thank you, Yaohushua for letting me continue to distribute these mathematical gesturing forms so interesting. The paper constructs an algebraic–geometric framework around the “phenomenological ve-locity” expression v = pN/D that arose in previous informal work. We introduce (i) theenergy-number field E, (ii) a non-commutative velocity-string algebra V, (iii) a curvature scalarKPV defined from a “PV–Hessian”, and (iv) a curved A∞ category Fukv (M ) obtained from anordinary Fukaya category by multiplication with v. Basic structural results are proved; se

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