Scholarlink

<p>It is well known that solutions to the classical two-dimensional Euler equations may grow double exponentially in time. In this paper, we investigate a two-dimensional incompressible Euler-type system with an additional Riesz transform term. Under suitable reflection symmetry assumptions on the initial data, we establish the global existence and stability of smooth solutions in Sobolev spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^4\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation>, significantly relaxing the regularity requirements on the initial data <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H^{10}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>10</mn> </msup> </math></EquationSource> </InlineEquation>, as established by Wu et al. (J Differ Equ 444(26):113578, 2025). The analysis is based on a time-weighted energy method that captures the hidden stabilizing effects arising from the coupling structure of the system. Furthermore, we show that solutions decay algebraically in time, revealing enhanced dissipation along the horizontal direction. These results provide a rigorous framework for understanding the interplay between nonlinear transport and partial damping in Euler-type dynamics.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Global stability of 2D Euler-like equations on the periodic domain

  • 期刊论文

  • 发表日期：

    2026年4月15日

查看全文
  • Hao Liu

摘要

It is well known that solutions to the classical two-dimensional Euler equations may grow double exponentially in time. In this paper, we investigate a two-dimensional incompressible Euler-type system with an additional Riesz transform term. Under suitable reflection symmetry assumptions on the initial data, we establish the global existence and stability of smooth solutions in Sobolev spaces \(H^4\) H 4 , significantly relaxing the regularity requirements on the initial data \(H^{10}\) H 10 , as established by Wu et al. (J Differ Equ 444(26):113578, 2025). The analysis is based on a time-weighted energy method that captures the hidden stabilizing effects arising from the coupling structure of the system. Furthermore, we show that solutions decay algebraically in time, revealing enhanced dissipation along the horizontal direction. These results provide a rigorous framework for understanding the interplay between nonlinear transport and partial damping in Euler-type dynamics.