# Strong convergence of the vorticity for the 2D Euler Equations in the inviscid limit

Ciampa, Gennaro and Crippa, Gianluca and Spirito, Stefano. (2021) Strong convergence of the vorticity for the 2D Euler Equations in the inviscid limit. Preprints Fachbereich Mathematik, 2021 (12).

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Official URL: https://edoc.unibas.ch/82583/

In this paper we prove the uniform-in-time $L^p$ convergence in the inviscid limit of a family $\omega^\nu$ of solutions of the $2D$ Navier-Stokes equations towards a renormalized/Lagrangian solution $\omega$ 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 $\omega^\nu$ to $\omega$ in $L^p$. Finally, we show that solutions of the Euler equations with $L^p$ 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.