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<p>In the vanishing viscosity limit from the Navier–Stokes to Euler equations on domains with boundaries, a main difficulty comes from the mismatch of boundary conditions and, consequently, the possible formation of a boundary layer. Within a purely interior framework, Constantin and Vicol showed that the two-dimensional viscosity limit is justified for any arbitrary but finite time under the assumption that on each compactly contained subset of the domain, the enstrophies are bounded uniformly along the viscosity sequence. Within this framework, we upgrade to local strong convergence of the vorticities under a similar assumption on the <i>p</i>-enstrophies, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p&gt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. The key novel idea is the analysis of the evolution of the weak convergence defect.</p>

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Strong Convergence of Vorticities in the 2D Viscosity Limit on a Bounded Domain

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月24日

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  • Christian Seis,
  • Emil Wiedemann,
  • Jakub Woźnicki

摘要

In the vanishing viscosity limit from the Navier–Stokes to Euler equations on domains with boundaries, a main difficulty comes from the mismatch of boundary conditions and, consequently, the possible formation of a boundary layer. Within a purely interior framework, Constantin and Vicol showed that the two-dimensional viscosity limit is justified for any arbitrary but finite time under the assumption that on each compactly contained subset of the domain, the enstrophies are bounded uniformly along the viscosity sequence. Within this framework, we upgrade to local strong convergence of the vorticities under a similar assumption on the p-enstrophies, \(p>2\) p > 2 . The key novel idea is the analysis of the evolution of the weak convergence defect.