Global well-posedness and decay estimates of strong solutions to the nonhomogeneous Boussinesq equations for magnetohydrodynamics convection. Issue 5 (October 2021)

• Record Type: Journal Article
• Authors: Zhong, Xin
• Is Part Of: Proceedings. Volume 151:Issue 5(2021)
• Page Start: 1543
• Page End: 1567
• Publication Date: 2021-10
• Subjects: Nonhomogeneous Boussinesq-MHD equations -- global well-posedness -- decay estimates -- large initial data -- vacuum; 35B65 -- 35Q35 -- 76D03; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2020.72
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : We deal with an initial boundary value problem of nonhomogeneous Boussinesq equations for magnetohydrodynamics convection in two-dimensional domains. We prove that there is a unique global strong solution. Moreover, we show that the temperature converges exponentially to zero in H 1 as time goes to infinity. In particular, the initial data can be arbitrarily large and vacuum is allowed. Our analysis relies on energy method and a lemma of Desjardins (Arch. Rational Mech. Anal. 137:135–158, 1997).