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nonhomogeneous boussinesq-mhd equations

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Global well-posedness and decay estimates of strong solutions to the nonhomogeneous Boussinesq equations for magnetohydrodynamics convection
Part of
Xin Zhong
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 5 / October 2021

Published online by Cambridge University Press:

15 September 2020, pp. 1543-1567

Print publication:

October 2021
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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).