Inviscid Limit of Vorticity Distributions in the Yudovich Class. Issue 1 (20th September 2020)

• Record Type: Journal Article
• Authors: Constantin, Peter; Drivas, Theodore D.; Elgindi, Tarek M.
• Is Part Of: Communications on pure and applied mathematics. Volume 75:Issue 1(2022)
• Page Start: 60
• Page End: 82
• Publication Date: 2020-09-20
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21940
• Languages: English
• ISSNs: 0010-3640

Abstract

Abstract: We prove that given initial data ω 0 ∈ L ∞ T 2, forcing g ∈ L ∞ 0, T ; L ∞ T 2, and any T > 0, the solutions u ν of Navier‐Stokes converge strongly in L ∞ 0, T ; W 1, p T 2 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 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. © 2020 Wiley Periodicals LLC.