Global existence and decay estimates of solutions to the MHD–Boussinesq system with stratification effects*This work was supported by National Natural Science Foundation of China, NSFC (No.: 11926316, 11531010, 12071391). (1st December 2022)

• Record Type: Journal Article
• Authors: Li, Xinliang; Tan, Zhong; Xu, Saiguo
• Is Part Of: Nonlinearity. Volume 35:Number 12(2022)
• Page Start: 6067
• Page End: 6097
• Publication Date: 2022-12-01
• Subjects: global well-posedness -- time decay rates -- MHD–Boussinesq system -- stratification effects; 35Q35 -- 35B40 -- 76D03; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac93e0
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we consider the inviscid Boussinesq system under the presence of magnetic field in porous media. We firstly proved the global well-posedness and large time behaviour of solutions in the whole space R 3 . Precisely, when the H 3 norm of initial data is small, but the higher order derivatives can be arbitrary large, the system is globally well-posed by pure energy method. Moreover, by a set of mature negative Sobolev and Besov space interpolation methods, the L p − L 2 (1 ⩽ p ⩽ 2) type of the optimal time decay rates are obtained without any smallness assumption on the L p norm of the initial data. At last, we derive a global weak solution with large initial data and give an explicit decay rate of the solution in R 2 . Our results mathematically explain the stable phenomenon of the system with stratification effects.