In this paper we prove the uniform-in-time Lp convergence in the inviscid limit of a family ων of solutions of the 2D Navier–Stokes equations towards a renormalized/Lagrangian solution ω of the Euler equations. We also prove that, in the class of solutions with bounded vorticity, it is possible to obtain a rate for the convergence of ων to ω in Lp. Finally, we show that solutions of the Euler equations with Lp vorticity, obtained in the vanishing viscosity limit, conserve the kinetic energy. The proofs are given by using both a (stochastic) Lagrangian approach and an Eulerian approach.

Strong Convergence of the Vorticity for the 2D Euler Equations in the Inviscid Limit

Ciampa G.;Spirito S.
2021

Abstract

In this paper we prove the uniform-in-time Lp convergence in the inviscid limit of a family ων of solutions of the 2D Navier–Stokes equations towards a renormalized/Lagrangian solution ω of the Euler equations. We also prove that, in the class of solutions with bounded vorticity, it is possible to obtain a rate for the convergence of ων to ω in Lp. Finally, we show that solutions of the Euler equations with Lp vorticity, obtained in the vanishing viscosity limit, conserve the kinetic energy. The proofs are given by using both a (stochastic) Lagrangian approach and an Eulerian approach.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/177894
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