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- W4307244446 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 <?CDATA ${mathbb{R}}^{3}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:msup> <mml:mrow> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> . 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 <?CDATA ${mathbb{R}}^{2}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:msup> <mml:mrow> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> . Our results mathematically explain the stable phenomenon of the system with stratification effects." @default.
- W4307244446 created "2022-10-30" @default.
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- W4307244446 date "2022-10-20" @default.
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- W4307244446 title "Global existence and decay estimates of solutions to the MHD–Boussinesq system with stratification effects*" @default.
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- W4307244446 doi "https://doi.org/10.1088/1361-6544/ac93e0" @default.
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