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<p>In this paper, we establish the global regularity of 2-dimensional tropical climate model in Sobolev space <i>H</i><sup>1</sup>(ℝ<sup>2</sup>). The system considered here has fractional dissipation Λ<sup>2<i>α</i></sup><i>u</i>, and we add exponential damping <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((e^{{|v|}^{2}}-1)v\)</EquationSource> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mi>v</mi> <mo>,</mo> <mi>r</mi> </math></EquationSource> </InlineEquation> or general damping ¦<i>v</i>¦<sup><i>gB-1</i></sup><i>v</i> on the first baroclinic mode of velocity to cope with the difficulty of lack of dissipation. Meanwhile, we also establish the global regularity for 2-dimensional MHD equations with similar dissipation and damping on the velocity field <i>u</i> and magnetic field <i>b</i>, respectively.</p>

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The Global Regularity of 2D Tropical Climate Model and 2D MHD Equations

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Xia Chen,
  • Bao-quan Yuan

摘要

In this paper, we establish the global regularity of 2-dimensional tropical climate model in Sobolev space H1(ℝ2). The system considered here has fractional dissipation Λ2αu, and we add exponential damping \((e^{{|v|}^{2}}-1)v\) ( e | v | 2 − 1 ) v , r or general damping ¦v¦gB-1v on the first baroclinic mode of velocity to cope with the difficulty of lack of dissipation. Meanwhile, we also establish the global regularity for 2-dimensional MHD equations with similar dissipation and damping on the velocity field u and magnetic field b, respectively.