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Non-autonomous boundary value problems on the real line
Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models
1. | Kharkov University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov, Ukraine |
2. | University of Virginia, Department of Mathematics, Charlottesville, VA 22901 |
[1] |
Igor Chueshov, Alexey Shcherbina. Semi-weak well-posedness and attractors for 2D Schrödinger-Boussinesq equations. Evolution Equations & Control Theory, 2012, 1 (1) : 57-80. doi: 10.3934/eect.2012.1.57 |
[2] |
Renhui Wan. Global well-posedness for the 2D Boussinesq equations with a velocity damping term. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2709-2730. doi: 10.3934/dcds.2019113 |
[3] |
Daniela De Silva, Nataša Pavlović, Gigliola Staffilani, Nikolaos Tzirakis. Global well-posedness for a periodic nonlinear Schrödinger equation in 1D and 2D. Discrete & Continuous Dynamical Systems - A, 2007, 19 (1) : 37-65. doi: 10.3934/dcds.2007.19.37 |
[4] |
Thomas Y. Hou, Congming Li. Global well-posedness of the viscous Boussinesq equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 1-12. doi: 10.3934/dcds.2005.12.1 |
[5] |
Magdalena Czubak, Nina Pikula. Low regularity well-posedness for the 2D Maxwell-Klein-Gordon equation in the Coulomb gauge. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1669-1683. doi: 10.3934/cpaa.2014.13.1669 |
[6] |
Shinya Kinoshita. Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1479-1504. doi: 10.3934/dcds.2018061 |
[7] |
Elaine Cozzi, James P. Kelliher. Well-posedness of the 2D Euler equations when velocity grows at infinity. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2361-2392. doi: 10.3934/dcds.2019100 |
[8] |
Saoussen Sokrani. On the global well-posedness of 3-D Boussinesq system with partial viscosity and axisymmetric data. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1613-1650. doi: 10.3934/dcds.2019072 |
[9] |
Tianwen Luo, Tao Tao, Liqun Zhang. Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 1-29. doi: 10.3934/dcds.2019230 |
[10] |
Wenru Huo, Aimin Huang. The global attractor of the 2d Boussinesq equations with fractional Laplacian in subcritical case. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2531-2550. doi: 10.3934/dcdsb.2016059 |
[11] |
Daniel Coutand, J. Peirce, Steve Shkoller. Global well-posedness of weak solutions for the Lagrangian averaged Navier-Stokes equations on bounded domains. Communications on Pure & Applied Analysis, 2002, 1 (1) : 35-50. doi: 10.3934/cpaa.2002.1.35 |
[12] |
Seckin Demirbas. Local well-posedness for 2-D Schrödinger equation on irrational tori and bounds on Sobolev norms. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1517-1530. doi: 10.3934/cpaa.2017072 |
[13] |
Qunyi Bie, Qiru Wang, Zheng-An Yao. On the well-posedness of the inviscid Boussinesq equations in the Besov-Morrey spaces. Kinetic & Related Models, 2015, 8 (3) : 395-411. doi: 10.3934/krm.2015.8.395 |
[14] |
Xin Zhong. Global well-posedness to the cauchy problem of two-dimensional density-dependent boussinesq equations with large initial data and vacuum. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6713-6745. doi: 10.3934/dcds.2019292 |
[15] |
Gaocheng Yue, Chengkui Zhong. On the global well-posedness to the 3-D Navier-Stokes-Maxwell system. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5817-5835. doi: 10.3934/dcds.2016056 |
[16] |
Zhaohi Huo, Yueling Jia, Qiaoxin Li. Global well-posedness for the 3D Zakharov-Kuznetsov equation in energy space $H^1$. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1797-1851. doi: 10.3934/dcdss.2016075 |
[17] |
Gaocheng Yue, Chengkui Zhong. On the global well-posedness to the 3-D incompressible anisotropic magnetohydrodynamics equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5801-5815. doi: 10.3934/dcds.2016055 |
[18] |
Xiaoping Zhai, Yongsheng Li, Wei Yan. Global well-posedness for the 3-D incompressible MHD equations in the critical Besov spaces. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1865-1884. doi: 10.3934/cpaa.2015.14.1865 |
[19] |
Edriss S. Titi, Saber Trabelsi. Global well-posedness of a 3D MHD model in porous media. Journal of Geometric Mechanics, 2019, 11 (4) : 621-637. doi: 10.3934/jgm.2019031 |
[20] |
Myeongju Chae, Soonsik Kwon. Global well-posedness for the $L^2$-critical Hartree equation on $\mathbb{R}^n$, $n\ge 3$. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1725-1743. doi: 10.3934/cpaa.2009.8.1725 |
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