文献类型：期刊文献

英文题名：STABILITY AND LARGE-TIME BEHAVIOR ON 3D INCOMPRESSIBLE MHD EQUATIONS WITH PARTIAL DISSIPATION NEAR A BACKGROUND MAGNETIC FIELD

作者：Lin, Hongxia[1]; Wu, Jiahong[2]; Zhu, Yi[3]

机构：[1] College of Mathematics and Physics, Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu, 610059, China; [2] Department of Mathematics, Oklahoma State University, Stillwater, OK, 74078, United States; [3] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2022

外文期刊名：arXiv

收录：EI(收录号：20220424333)

语种：英文

外文关键词：Anisotropy - Decay (organic) - Diffusion in liquids - Magnetohydrodynamics - Viscous flow

摘要：Physical experiments and numerical simulations have observed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and damps electrically conducting fluids. This paper intends to establish this phenomenon as a mathematically rigorous fact on a magnetohydrodynamic (MHD) system with anisotropic dissipation in 3. The velocity equation in this system is the 3D Navier-Stokes equation with dissipation only in the x1-direction while the magnetic field obeys the induction equation with magnetic diffusion in two horizontal directions. We establish that any perturbation near the background magnetic field (0, 1, 0) is globally stable in the Sobolev setting H3(3). In addition, explicit decay rates in H2(3) are also obtained. When there is no presence of the magnetic field, the 3D anisotropic Navier-Stokes equation in 3 is not well understood and the small data global well-posedness remains an intriguing open problem. This paper reveals the mechanism of how the magnetic field generates enhanced dissipation and helps stabilize the fluid.MSC Codes 35B35 ? 2022, CC BY.