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<p>In this study, the inviscid limit to the 2D-dissipative quasi-geostrophic equations is the topic of discussion. A sequence of solutions for the quasi-geostrophic equations with initial data <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\theta ^0_n \in H^{s}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>θ</mi> <mi>n</mi> <mn>0</mn> </msubsup> <mo>∈</mo> <msup> <mi>H</mi> <mi>s</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> is shown to converge to a solution of the critical dissipative quasi-geostrophic equation when the viscosity vanishes. This is demonstrated via the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H^{s}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mi>s</mi> </msup> </math></EquationSource> </InlineEquation>-convergence. Furthermore, the optimal rate of this convergence is given by utilizing standard energy estimates and taking the Sobolev embedding into consideration.</p>

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Inviscid limit for the sub-critical dissipative quasi-geostrophic equations in the Sobolev spaces

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • Moez Benhamed

摘要

In this study, the inviscid limit to the 2D-dissipative quasi-geostrophic equations is the topic of discussion. A sequence of solutions for the quasi-geostrophic equations with initial data \(\theta ^0_n \in H^{s}\) θ n 0 ∈ H s is shown to converge to a solution of the critical dissipative quasi-geostrophic equation when the viscosity vanishes. This is demonstrated via the \(H^{s}\) H s -convergence. Furthermore, the optimal rate of this convergence is given by utilizing standard energy estimates and taking the Sobolev embedding into consideration.