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Journal articles on the topic 'Local well-posedness'

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1

Willison, Steven. "Local well-posedness in Lovelock gravity." Classical and Quantum Gravity 32, no. 2 (December 19, 2014): 022001. http://dx.doi.org/10.1088/0264-9381/32/2/022001.

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2

Isaza, Pedro, and Jorge Mejía. "Local well-posedness and quantitative ill-posedness for the Ostrovsky equation." Nonlinear Analysis: Theory, Methods & Applications 70, no. 6 (March 2009): 2306–16. http://dx.doi.org/10.1016/j.na.2008.03.010.

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3

CHEN, Zeqian. "Local Well-posedness for Gross-Pitaevskii Hierarchies." Acta Analysis Functionalis Applicata 15, no. 4 (2013): 291. http://dx.doi.org/10.3724/sp.j.1160.2013.00291.

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4

Kishimoto, Nobu. "Unconditional local well-posedness for periodic NLS." Journal of Differential Equations 274 (February 2021): 766–87. http://dx.doi.org/10.1016/j.jde.2020.10.025.

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5

Hille, Sander C. "Local Well-posedness of Kinetic Chemotaxis Models." Journal of Evolution Equations 8, no. 3 (May 20, 2008): 423–48. http://dx.doi.org/10.1007/s00028-008-0358-7.

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6

Shatah, Jalal, and Chongchun Zeng. "Local Well-Posedness for Fluid Interface Problems." Archive for Rational Mechanics and Analysis 199, no. 2 (June 30, 2010): 653–705. http://dx.doi.org/10.1007/s00205-010-0335-5.

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7

Racke, Reinhard, and Jürgen Saal. "Hyperbolic Navier-Stokes equations I: Local well-posedness." Evolution Equations and Control Theory 1, no. 1 (March 2012): 195–215. http://dx.doi.org/10.3934/eect.2012.1.195.

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8

Liu, Yongqin, and Weike Wang. "Local well-posedness of a new integrable equation." Nonlinear Analysis: Theory, Methods & Applications 64, no. 11 (June 2006): 2516–26. http://dx.doi.org/10.1016/j.na.2005.08.030.

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9

Zhong, Xin, Xing-Ping Wu, and Chun-Lei Tang. "Local well-posedness for the homogeneous Euler equations." Nonlinear Analysis: Theory, Methods & Applications 74, no. 11 (July 2011): 3829–48. http://dx.doi.org/10.1016/j.na.2011.03.037.

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10

Dörfler, Willy, Hannes Gerner, and Roland Schnaubelt. "Local well-posedness of a quasilinear wave equation." Applicable Analysis 95, no. 9 (September 23, 2015): 2110–23. http://dx.doi.org/10.1080/00036811.2015.1089236.

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11

Escobedo, M., and J. J. L. Velázquez. "Local well posedness for a linear coagulation equation." Transactions of the American Mathematical Society 365, no. 4 (October 4, 2012): 1743–808. http://dx.doi.org/10.1090/s0002-9947-2012-05576-0.

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12

Fang, Yung-Fu, and Kuan-Hsiang Wang. "Local well-posedness for the quantum Zakharov system." Communications in Mathematical Sciences 18, no. 5 (2020): 1383–411. http://dx.doi.org/10.4310/cms.2020.v18.n5.a9.

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13

Goodchild, Sam, and Hang Yang. "Local well-posedness of a nonlocal Burgers’ equation." Involve, a Journal of Mathematics 9, no. 1 (January 1, 2016): 67–82. http://dx.doi.org/10.2140/involve.2016.9.67.

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14

Fajman, David. "Local Well-Posedness for the Einstein--Vlasov System." SIAM Journal on Mathematical Analysis 48, no. 5 (January 2016): 3270–321. http://dx.doi.org/10.1137/15m1030236.

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15

Wang, Yuzhao. "Local well-posedness for hyperbolic–elliptic Ishimori equation." Journal of Differential Equations 252, no. 9 (May 2012): 4625–55. http://dx.doi.org/10.1016/j.jde.2012.01.022.

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16

Köhne, Matthias, and Daniel Lengeler. "Local well-posedness for relaxational fluid vesicle dynamics." Journal of Evolution Equations 18, no. 4 (July 19, 2018): 1787–818. http://dx.doi.org/10.1007/s00028-018-0461-3.

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17

Nakamura, Makoto, and Takeshi Wada. "Local well-posedness for the Maxwell-Schrödinger equation." Mathematische Annalen 332, no. 3 (May 2005): 565–604. http://dx.doi.org/10.1007/s00208-005-0637-3.

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18

Akhunov, Timur. "Local well-posedness of quasi-linear systems generalizing KdV." Communications on Pure and Applied Analysis 12, no. 2 (September 2012): 899–921. http://dx.doi.org/10.3934/cpaa.2013.12.899.

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19

Ibrahim, Slim, Rym Jrad, Mohamed Majdoub, and Tarek Saanouni. "Local well posedness of a 2D semilinear heat equation." Bulletin of the Belgian Mathematical Society - Simon Stevin 21, no. 3 (August 2014): 535–51. http://dx.doi.org/10.36045/bbms/1407765888.

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20

Esfahani, Amin, and Luiz Gustavo Farah. "Local well-posedness for the sixth-order Boussinesq equation." Journal of Mathematical Analysis and Applications 385, no. 1 (January 2012): 230–42. http://dx.doi.org/10.1016/j.jmaa.2011.06.038.

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21

Marinelli, Carlo. "LOCAL WELL-POSEDNESS OF MUSIELA’S SPDE WITH LÉVY NOISE." Mathematical Finance 20, no. 3 (June 7, 2010): 341–63. http://dx.doi.org/10.1111/j.1467-9965.2010.00403.x.

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22

Kolev, Boris. "Local well-posedness of the EPDiff equation: A survey." Journal of Geometric Mechanics 9, no. 2 (2017): 167–89. http://dx.doi.org/10.3934/jgm.2017007.

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23

Levermore, C. David, and Weiran Sun. "Local well-posedness of a dispersive Navier-Stokes system." Indiana University Mathematics Journal 60, no. 2 (2011): 517–76. http://dx.doi.org/10.1512/iumj.2011.60.4179.

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24

Israwi, Samer, and Raafat Talhouk. "Local well-posedness of a nonlinear KdV-type equation." Comptes Rendus Mathematique 351, no. 23-24 (December 2013): 895–99. http://dx.doi.org/10.1016/j.crma.2013.10.032.

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25

Zhang, Yinghui. "Local well-posedness of the free-surface incompressible elastodynamics." Journal of Differential Equations 268, no. 11 (May 2020): 6971–7011. http://dx.doi.org/10.1016/j.jde.2019.11.075.

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26

Jang, Juhi. "Local Well-Posedness of Dynamics of Viscous Gaseous Stars." Archive for Rational Mechanics and Analysis 195, no. 3 (July 28, 2009): 797–863. http://dx.doi.org/10.1007/s00205-009-0253-6.

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27

Kishimoto, Nobu. "Sharp local well-posedness for the “good” Boussinesq equation." Journal of Differential Equations 254, no. 6 (March 2013): 2393–433. http://dx.doi.org/10.1016/j.jde.2012.12.008.

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28

Escher, Joachim, and Patrick Guidotti. "Local well-posedness for a quasi-stationary droplet model." Calculus of Variations and Partial Differential Equations 54, no. 1 (January 24, 2015): 1147–60. http://dx.doi.org/10.1007/s00526-015-0820-7.

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29

Kenig, Carlos E., and Gigliola Staffilani. "Local well-posedness for higher order nonlinear dispersive systems." Journal of Fourier Analysis and Applications 3, no. 4 (July 1997): 417–33. http://dx.doi.org/10.1007/bf02649104.

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30

Linares, Felipe, and Aniura Milanés. "Local and global well-posedness for the Ostrovsky equation." Journal of Differential Equations 222, no. 2 (March 2006): 325–40. http://dx.doi.org/10.1016/j.jde.2005.07.023.

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31

Aloui, Lassaad, and Slim Tayachi. "Local well-posedness for the inhomogeneous nonlinear Schrödinger equation." Discrete & Continuous Dynamical Systems 41, no. 11 (2021): 5409. http://dx.doi.org/10.3934/dcds.2021082.

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<p style='text-indent:20px;'>We consider the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation <inline-formula><tex-math id="M1">\begin{document}$ i\partial_t u +\Delta u = \mu |x|^{-b}|u|^\alpha u,\; u(0)\in H^s({\mathbb R}^N),\; N\geq 1,\; \mu\in {\mathbb C},\; \; b&gt;0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ \alpha&gt;0. $\end{document}</tex-math></inline-formula> Only partial results are known for the local existence in the subcritical case <inline-formula><tex-math id="M3">\begin{document}$ \alpha&lt;(4-2b)/(N-2s) $\end{document}</tex-math></inline-formula> and much more less in the critical case <inline-formula><tex-math id="M4">\begin{document}$ \alpha = (4-2b)/(N-2s). $\end{document}</tex-math></inline-formula> In this paper, we develop a local well-posedness theory for the both cases. In particular, we establish new results for the continuous dependence and for the unconditional uniqueness. Our approach provides simple proofs and allows us to obtain lower bounds of the blowup rate and of the life span. The Lorentz spaces and the Strichartz estimates play important roles in our argument. In particular this enables us to reach the critical case and to unify results for <inline-formula><tex-math id="M5">\begin{document}$ b = 0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ b&gt;0. $\end{document}</tex-math></inline-formula></p>
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32

Xu, Xiaojing. "Local well-posedness and ill-posedness for the fractal Burgers equation in homogeneous Sobolev spaces." Mathematical Methods in the Applied Sciences 32, no. 3 (February 2009): 359–70. http://dx.doi.org/10.1002/mma.1046.

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33

FANG, DAOYUAN, and CHENGBO WANG. "LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u = uk(∂u)α." Chinese Annals of Mathematics 26, no. 03 (July 2005): 361–78. http://dx.doi.org/10.1142/s0252959905000294.

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34

Huo, Zhaohui, and Yueling Jia. "LOW-REGULARITY SOLUTIONS FOR THE OSTROVSKY EQUATION." Proceedings of the Edinburgh Mathematical Society 49, no. 1 (February 2006): 87–100. http://dx.doi.org/10.1017/s0013091504000938.

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AbstractThe well-posedness of the Ostrovsky equation is considered. Local well-posedness for data in $\tilde{H}^s(\mathbb{R})$ $(s\geq-\frac{1}{8})$ and global well-posedness for data in $\tilde{L}^{2}(\mathbb{R})$ are obtained.
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35

Germain, Pierre, Slim Ibrahim, and Nader Masmoudi. "Well-posedness of the Navier—Stokes—Maxwell equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 1 (January 30, 2014): 71–86. http://dx.doi.org/10.1017/s0308210512001242.

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We study the local and global well-posedness of a full system of magnetohydrodynamic equations. The system is a coupling of the incompressible Navier—Stokes equations with the Maxwell equations through the Lorentz force and Ohm's law for the current. We show the local existence of mild solutions for arbitrarily large data in a space similar to the scale-invariant spaces classically used for Navier—Stokes. These solutions are global if the initial data are small enough. Our results not only simplify and unify the proofs for the space dimensions 2 and 3, but also refine those in [8]. The main simplification comes from an a prioriLt2 (Lx∞) estimate for solutions of the forced Navier—Stokes equations.
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36

Smith, Hart, and Daniel Tataru. "Sharp local well-posedness results for the nonlinear wave equation." Annals of Mathematics 162, no. 1 (July 1, 2005): 291–366. http://dx.doi.org/10.4007/annals.2005.162.291.

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37

Li, Junfeng, and Shaoguang Shi. "Local well-posedness for the dispersion generalized periodic KdV equation." Journal of Mathematical Analysis and Applications 379, no. 2 (July 2011): 706–18. http://dx.doi.org/10.1016/j.jmaa.2011.01.026.

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38

Barros, Amauri. "Local well-posedness for the super Korteweg–de Vries equation." Nonlinear Analysis: Theory, Methods & Applications 68, no. 6 (March 2008): 1581–94. http://dx.doi.org/10.1016/j.na.2006.12.034.

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39

Bényi, Árpád, and Kasso A. Okoudjou. "Local well-posedness of nonlinear dispersive equations on modulation spaces." Bulletin of the London Mathematical Society 41, no. 3 (April 3, 2009): 549–58. http://dx.doi.org/10.1112/blms/bdp027.

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40

LIU, YACHENG, and RUNZHANG XU. "LOCAL WELL POSEDNESS OF CAUCHY PROBLEM FOR VISCOUS DIFFUSION EQUATIONS." International Journal of Mathematics 20, no. 04 (April 2009): 509–19. http://dx.doi.org/10.1142/s0129167x09005364.

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In this paper, we study the Cauchy problem of multi-dimensional viscous diffusion equations. By using an equivalent integral equations, we get the existence of local Wk,p solutions. And we prove the finite time blow up of solutions under appropriate conditions.
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41

Ionescu, Alexandru D., and Carlos E. Kenig. "Well-posedness and local smoothing of solutions of Schrödinger equations." Mathematical Research Letters 12, no. 2 (2005): 193–205. http://dx.doi.org/10.4310/mrl.2005.v12.n2.a5.

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42

Zheng, Yunrui. "Local well-posedness for the Bénard convection without surface tension." Communications in Mathematical Sciences 15, no. 4 (2017): 903–56. http://dx.doi.org/10.4310/cms.2017.v15.n4.a2.

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43

Jang, Juhi, Ian Tice, and Yanjin Wang. "The Compressible Viscous Surface-Internal Wave Problem: Local Well-Posedness." SIAM Journal on Mathematical Analysis 48, no. 4 (January 2016): 2602–73. http://dx.doi.org/10.1137/15m1036026.

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44

Su, Xiaoyan, Shiliang Zhao, and Miao Li. "Local well-posedness of semilinear space-time fractional Schrödinger equation." Journal of Mathematical Analysis and Applications 479, no. 1 (November 2019): 1244–65. http://dx.doi.org/10.1016/j.jmaa.2019.06.077.

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45

Huang, Yongting, Cheng-Jie Liu, and Tong Yang. "Local-in-time well-posedness for compressible MHD boundary layer." Journal of Differential Equations 266, no. 6 (March 2019): 2978–3013. http://dx.doi.org/10.1016/j.jde.2018.08.052.

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46

Hunter, John K., Jingyang Shu, and Qingtian Zhang. "Local Well-Posedness of an Approximate Equation for SQG Fronts." Journal of Mathematical Fluid Mechanics 20, no. 4 (August 31, 2018): 1967–84. http://dx.doi.org/10.1007/s00021-018-0396-z.

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47

Fan, Jishan, and Yong Zhou. "Uniform local well-posedness for the density-dependent magnetohydrodynamic equations." Applied Mathematics Letters 24, no. 11 (November 2011): 1945–49. http://dx.doi.org/10.1016/j.aml.2011.05.027.

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48

Oh, Seungly, and Atanas Stefanov. "Improved local well-posedness for the periodic “good” Boussinesq equation." Journal of Differential Equations 254, no. 10 (May 2013): 4047–65. http://dx.doi.org/10.1016/j.jde.2013.02.006.

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49

Germain, Pierre, Alexandru D. Ionescu, and Minh-Binh Tran. "Optimal local well-posedness theory for the kinetic wave equation." Journal of Functional Analysis 279, no. 4 (September 2020): 108570. http://dx.doi.org/10.1016/j.jfa.2020.108570.

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50

Allen, Paul T., Lars Andersson, and Alvaro Restuccia. "Local Well-Posedness for Membranes in the Light Cone Gauge." Communications in Mathematical Physics 301, no. 2 (October 17, 2010): 383–410. http://dx.doi.org/10.1007/s00220-010-1141-5.

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