Global well‐posedness of 3D incompressible inhomogeneous magnetohydrodynamic equations. (30th August 2022)

• Record Type: Journal Article
• Authors: Huang, Tian; Qian, Chenyin
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 2(2023)
• Page Start: 2906
• Page End: 2940
• Publication Date: 2022-08-30
• Subjects: Besov spaces -- inhomogeneous MHD equations -- Littlewood–Paley theory -- well‐posedness; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8679
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we investigate the 3D inhomogeneous incompressible magnetohydrodynamic (MHD) system. By the assumption of the smallness of initial velocity and magnetic fluids in the critical Besov space, the local and global well‐posedness of 3D inhomogeneous incompressible equations is obtained. It improves some previous results of MHD equations by generalizing the range of exponent p $$ p $$ in Besov spaces B ˙ p, 1 3 / p − 1 $$ {\dot{B}}_{p, 1}^{3/p-1} $$ with 1 < p < 6 $$ 1<p<6 $$ . Besides, the initial density belongs to the critical Besov space B q, 1 3 / q $$ {B}_{q, 1}^{3/q} $$ with 1 < q < 6 $$ 1<q<6 $$, and it is removed the additional restriction of 1 < q ≤ p $$ 1<q\le p $$, which is an important condition in some previous results for both 3D inhomogeneous incompressible Navier–Stokes equations and MHD system.