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<p>In this paper, we prove the local well-posedness of the quasi-geostrophic equations in the Gevrey-Sobolev space. Moreover, we analyze the possible blow-up behavior of these solutions. In addition, if the initial data is assumed to be small enough, this paper proves the existence of global in time solution. Furthermore, it is shown that the Gevrey norm of the solution decays to zero as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(t\rightarrow \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo stretchy="false">→</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Well-Posedness, blow-up criteria and asymptotic study of a global solution of super-critical quasi-geostrophic equation

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Chaala Katar

摘要

In this paper, we prove the local well-posedness of the quasi-geostrophic equations in the Gevrey-Sobolev space. Moreover, we analyze the possible blow-up behavior of these solutions. In addition, if the initial data is assumed to be small enough, this paper proves the existence of global in time solution. Furthermore, it is shown that the Gevrey norm of the solution decays to zero as \(t\rightarrow \infty \) t → ∞ .