一类二维MHD-Boussinesq方程组整体解的存在性
Existence of Global Solution to a Class of Two-Dimensional MHD-Boussinesq Equations
DOI: 10.12677/PM.2021.112027, PDF,   
作者: 秦文迪:青岛大学数学与统计学院,山东 青岛
关键词: MHD-Boussinesq方程组局部解整体解MHD-Boussinesq Equations Local Solution Global Solution
摘要: 本文证明了一类二维不可压缩MHD-Boussinesq方程组的初值问题在Hs(R2),s>2空间中存在唯一的整体强解。
Abstract: In this paper, we prove that there exists a unique global strong solution to the initial-value problem of a class of two-dimensional incompressible MHD-Boussinesq equations in Hs(R2),s>2.
文章引用:秦文迪. 一类二维MHD-Boussinesq方程组整体解的存在性[J]. 理论数学, 2021, 11(2): 192-200. https://doi.org/10.12677/PM.2021.112027

参考文献

[1] Hmidi, T. and Keraani, S. (2007) On the Global Well-Posedness of the Boussinesq System with Zero Viscosity. Indiana University Mathematics Journal, 58, 1591-1618. [Google Scholar] [CrossRef
[2] Larios, A. and Pei, Y. (2017) On the Local Well-Posedness and a Prodi-Serrin-Type Regularity Criterion of the Three- Dimensional MHD-Boussinesq System without Thermal Diffusion. Journal of Differential Equations, 263, 1419-1450. [Google Scholar] [CrossRef
[3] Zhai, X. and Chen, Z. (2018) Global Well-Posedness for the MHD-Boussinesq System with the Temperature-Dependent Viscosity. Nonlinear Analysis Real World Applications, 44, 260-282. [Google Scholar] [CrossRef
[4] Li, Z., Liu, P. and Niu, P. (2019) Global Well-Posedness and Large Time Asymptotic Behavior of Strong Solutions to the Cauchy Problem of the 2-D MHD Equation. arXiv: 1901.01384. [Google Scholar] [CrossRef
[5] Simon, J. (1990) Nonhomogeneous Viscous Incompressible Fluids: Existence of Velocity, Density, and Pressure. Siam Journal on Mathematical Analysis, 21, 1093-1117. [Google Scholar] [CrossRef
[6] Kenig, C.E., Ponce, G. and Vega, L. (1993) Well-Posedness and Scattering Results for the Generalized Korteweg-De Vries Equation via the Contraction Principle. Communications on Pure and Applied Mathematics, 46, 527-620. [Google Scholar] [CrossRef
[7] Wang, C. and Zhang, Z. (2011) Global Well-Posedness for the 2-D Boussinesq System with the Temperature-Dependent Viscosity and Thermal Diffusivity. Advances in Mathematics, 228, 43-62. [Google Scholar] [CrossRef