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Global well-posedness and decay estimates of strong solutions to the nonhomogeneous Boussinesq equations for magnetohydrodynamics convection

Part of: Incompressible viscous fluids Equations of mathematical physics and other areas of application Partial differential equations

Published online by Cambridge University Press:  15 September 2020

Xin Zhong
Xin Zhong*
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing400715, People's Republic of China ([email protected])
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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 H1 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).

Keywords

Nonhomogeneous Boussinesq-MHD equationsglobal well-posednessdecay estimateslarge initial datavacuum

MSC classification

Primary: 35B65: Smoothness and regularity of solutions
Secondary: 35Q35: PDEs in connection with fluid mechanics 76D03: Existence, uniqueness, and regularity theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 5 , October 2021 , pp. 1543 - 1567
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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Footnotes

This research was partially supported by National Natural Science Foundation of China (No. 11901474).

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