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<p>In this article, thanks to a detailed study of the Green function of Rayleigh’s equation near an extremum of the velocity of a shear layer, we study the asymptotic behavior of solutions to the linearized incompressible Euler equations and the so called “vorticity depletion property” discovered by Bouchet and Morita (Phys. D 239(12), 948–966, 2010). We, in particular, use a localization property of the solutions of Rayleigh’s equation near extrema of the velocity.</p>

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Asymptotic Behavior of Solutions of the Linearized Euler Equations Near a Shear Layer

  • 期刊论文

  • 发表日期：

    2026年4月9日

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  • Dongfen Bian,
  • Emmanuel Grenier

摘要

In this article, thanks to a detailed study of the Green function of Rayleigh’s equation near an extremum of the velocity of a shear layer, we study the asymptotic behavior of solutions to the linearized incompressible Euler equations and the so called “vorticity depletion property” discovered by Bouchet and Morita (Phys. D 239(12), 948–966, 2010). We, in particular, use a localization property of the solutions of Rayleigh’s equation near extrema of the velocity.