arXiv Analytics

Sign in

arXiv:1909.04651 [math.AP]AbstractReferencesReviewsResources

Inviscid limit of vorticity distributions in Yudovich class

Peter Constantin, Theodore D. Drivas, Tarek M. Elgindi

Published 2019-09-10Version 1

We prove that given initial data $\omega_0\in L^\infty(\mathbb{T}^2)$, forcing $g\in L^\infty(0,T; L^\infty(\mathbb{T}^2))$, and any $T>0$, the solutions $u^\nu$ of Navier-Stokes converge strongly in $L^\infty(0,T;W^{1,p}(\mathbb{T}^2))$ for any $p\in [1,\infty)$ to the unique Yudovich weak solution $u$ of the Euler equations. A consequence is that vorticity distribution functions converge to their inviscid counterparts. As a byproduct of the proof, we establish continuity of the Euler solution map for Yudovich solutions in the $L^p$ vorticity topology. The main tool in these proofs is a uniformly controlled loss of regularity property of the linear transport by Yudovich solutions. Our results provide a partial foundation for the Miller--Robert statistical equilibrium theory of vortices as it applies to slightly viscous fluids.

Related articles: Most relevant | Search more
arXiv:1410.4952 [math.AP] (Published 2014-10-18)
Remarks on the inviscid limit for the compressible flows
arXiv:1612.04645 [math.AP] (Published 2016-12-14)
A note on the inviscid limit of the incompressible MHD equations
arXiv:1004.4033 [math.AP] (Published 2010-04-23)
Inviscid Limit for Vortex Patches in A Bounded Domain