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- W4221036629 abstract "Abstract In this paper, some new $L^{p}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> gradient estimates are justified for the three-dimensional compressible magnetohydrodynamic equations in the whole space $mathbb{R}^{3}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:math> . The key to derive the estimate $|nabla textbf {u}|_{L^{3}}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mrow> <mml:mo>∥</mml:mo> <mml:mi>∇</mml:mi> <mml:mtext>u</mml:mtext> <mml:mo>∥</mml:mo> </mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:msub> </mml:math> is the “div-curl” decomposition technique. For regular initial data with small energy, we prove the existence of global solutions belonging to a new class of functions in which the uniqueness can be shown to hold." @default.
- W4221036629 created "2022-04-03" @default.
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- W4221036629 date "2022-03-09" @default.
- W4221036629 modified "2023-09-25" @default.
- W4221036629 title "Regularity and uniqueness for the 3D compressible magnetohydrodynamic equations" @default.
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- W4221036629 doi "https://doi.org/10.1186/s13661-022-01593-2" @default.
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