Publications [#361919] of Tarek M Elgindi

Papers Published

1. Constantin, P; Drivas, TD; Elgindi, TM, Inviscid Limit of Vorticity Distributions in the Yudovich Class, Communications on Pure and Applied Mathematics, vol. 75 no. 1 (January, 2022), pp. 60-82 [doi]
   (last updated on 2024/04/15)

   Abstract:
   We prove that given initial data (Formula presented.), forcing (Formula presented.) and any T > 0, the solutions uν of Navier-Stokes converge strongly in (Formula presented.) for any p ∈ [1, ∞) 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 by-product of the proof, we establish continuity of the Euler solution map for Yudovich solutions in the Lp 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. © 2020 Wiley Periodicals LLC.