Singular vorticity solutions of the incompressible Euler equation via inviscid limits

2013/08/28 by Joerg Kampen, Kampen, Joerg · 1 citation
Mathematics · Engineering · #Navier-Stokes equation solutions #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.1308.6082

Abstract

Singular vorticty solutions of the incompressible 3D-Euler equation are constructed which satisfy the BKM criterion (cf. [2]). The construction is done by inviscid limits of vorticity solutions of transformed incompressible Navier Stokes type equations with a damping potential term, where the latter equations admit a global regular solution for positive viscosity. The inviscid limit vorticity solution of the incompressible Euler vorticity equation becomes singular at a point of the boundary of a finite domain.

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• Some infinite matrix analysis, a Trotter product formula for dissipative\n operators, and an algorithm for the incompressible Navier-Stokes equation
• On an auto-controlled global existence scheme of the incompressible\n Navier Stokes equation

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