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Best constant of 3D Anisotropic Sobolev inequality and its applications
On the stability problem for the Boussinesq equations in weak-$L^p$ spaces
1. | Universidade Estadual de Campinas, Campinas, CEP 13083-970, Brazil |
2. | Universidad Nacional de Colombia, Sede Medellín, Medellín, A.A. 3840, Colombia |
[1] |
Elder J. Villamizar-Roa, Elva E. Ortega-Torres. On a generalized Boussinesq model around a rotating obstacle: Existence of strong solutions. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 825-847. doi: 10.3934/dcdsb.2011.15.825 |
[2] |
Zhijian Yang, Pengyan Ding, Xiaobin Liu. Attractors and their stability on Boussinesq type equations with gentle dissipation. Communications on Pure and Applied Analysis, 2019, 18 (2) : 911-930. doi: 10.3934/cpaa.2019044 |
[3] |
Chun-Hsiung Hsia, Tian Ma, Shouhong Wang. Rotating Boussinesq equations: Dynamic stability and transitions. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 99-130. doi: 10.3934/dcds.2010.28.99 |
[4] |
Yonggeun Cho, Tohru Ozawa. On small amplitude solutions to the generalized Boussinesq equations. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 691-711. doi: 10.3934/dcds.2007.17.691 |
[5] |
Liangliang Ma. Stability of hydrostatic equilibrium to the 2D fractional Boussinesq equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 863-882. doi: 10.3934/dcdsb.2021068 |
[6] |
Tong Tang, Hongjun Gao. Local strong solutions to the compressible viscous magnetohydrodynamic equations. Discrete and Continuous Dynamical Systems - B, 2016, 21 (5) : 1617-1633. doi: 10.3934/dcdsb.2016014 |
[7] |
José Luiz Boldrini, Jonathan Bravo-Olivares, Eduardo Notte-Cuello, Marko A. Rojas-Medar. Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations. Electronic Research Archive, 2021, 29 (1) : 1783-1801. doi: 10.3934/era.2020091 |
[8] |
Agissilaos G. Athanassoulis, Gerassimos A. Athanassoulis, Mariya Ptashnyk, Themistoklis Sapsis. Strong solutions for the Alber equation and stability of unidirectional wave spectra. Kinetic and Related Models, 2020, 13 (4) : 703-737. doi: 10.3934/krm.2020024 |
[9] |
Ruizhi Gong, Yuren Shi, Deng-Shan Wang. Linear stability of exact solutions for the generalized Kaup-Boussinesq equation and their dynamical evolutions. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 3355-3378. doi: 10.3934/dcds.2022018 |
[10] |
Claudia Valls. Stability of some waves in the Boussinesq system. Communications on Pure and Applied Analysis, 2006, 5 (4) : 929-939. doi: 10.3934/cpaa.2006.5.929 |
[11] |
Marta Lewicka, Mohammadreza Raoofi. A stability result for the Stokes-Boussinesq equations in infinite 3d channels. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2615-2625. doi: 10.3934/cpaa.2013.12.2615 |
[12] |
Siran Li, Jiahong Wu, Kun Zhao. On the degenerate boussinesq equations on surfaces. Journal of Geometric Mechanics, 2020, 12 (1) : 107-140. doi: 10.3934/jgm.2020006 |
[13] |
T. Tachim Medjo. Existence and uniqueness of strong periodic solutions of the primitive equations of the ocean. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1491-1508. doi: 10.3934/dcds.2010.26.1491 |
[14] |
Youcef Amirat, Kamel Hamdache. Strong solutions to the equations of flow and heat transfer in magnetic fluids with internal rotations. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3289-3320. doi: 10.3934/dcds.2013.33.3289 |
[15] |
Jochen Merker. Strong solutions of doubly nonlinear Navier-Stokes equations. Conference Publications, 2011, 2011 (Special) : 1052-1060. doi: 10.3934/proc.2011.2011.1052 |
[16] |
Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 395-415. doi: 10.3934/cpaa.2004.3.395 |
[17] |
Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115 |
[18] |
Yan Jia, Xingwei Zhang, Bo-Qing Dong. Remarks on the blow-up criterion for smooth solutions of the Boussinesq equations with zero diffusion. Communications on Pure and Applied Analysis, 2013, 12 (2) : 923-937. doi: 10.3934/cpaa.2013.12.923 |
[19] |
Shengfu Deng. Generalized multi-hump wave solutions of Kdv-Kdv system of Boussinesq equations. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 3671-3716. doi: 10.3934/dcds.2019150 |
[20] |
Tianwen Luo, Tao Tao, Liqun Zhang. Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3737-3765. doi: 10.3934/dcds.2019230 |
2020 Impact Factor: 1.916
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