Asymptotic behavior of solutions of the linearized Euler equations near a shear layer

2024/03/20 by Dongfen Bian, Bian, Dongfen, Emmanuel Grenier +1
Mathematics · Computer Science · #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2403.13549

Abstract

In this article, thanks to a new and detailed study of the Green's function of Rayleigh equation near the extrema of the velocity of a shear layer, we obtain optimal bounds on the asymptotic behaviour of solutions to the linearized incompressible Euler equations both in the whole plane, the half plane and the periodic case, and improve the description of the so called "vorticity depletion property" discovered by F. Bouchet and H. Morita by putting into light a localization property of the solutions of Rayleigh equation near an extremal velocity.

Related

• Singularities of Rayleigh equation
• Sharp bounds for the resolvent of linearized Navier Stokes equations in\n the half space around a shear profile
• Ill-posedness for the incompressible Euler equations in critical Sobolev spaces
• The limit α→ 0 of the α-Euler equations in the half plane with no-slip boundary conditions and vortex sheet initial data
• Linear inviscid damping and vorticity depletion for shear flows