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

Gianluca Crippa
University of Basel

I will discuss some recent results obtained with G. Ciampa (University of Padova) and Stefano Spirito (University of L'Aquila) on the strong $L^p$ convergence (uniformly in time) 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. In the class of solutions with bounded vorticity, it is possible to obtain a rate for the convergence of $\omega^\nu$ to $\omega$ in $L^p$. The proofs are given by using both a (stochastic) Lagrangian approach and an Eulerian approach.

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