Uniqueness of the 2D Euler equation on a corner domain with non-constant vorticity around the corner. (6th June 2022)

• Record Type: Journal Article
• Authors: Agrawal, Siddhant; Nahmod, Andrea R
• Is Part Of: Nonlinearity. Volume 35:Number 6(2022)
• Page Start: 2767
• Page End: 2808
• Publication Date: 2022-06-06
• Subjects: non smooth domain -- fluid mechanics -- 2D Euler equation; 35Q31, 76B03; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac586a
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider the 2D incompressible Euler equation on a corner domain Ω with angle νπ with 1 2 < ν < 1 . We prove that if the initial vorticity ω 0 ∈ L 1 (Ω) ∩ L ∞ (Ω) and if ω 0 is non-negative and supported on one side of the angle bisector of the domain, then the weak solutions are unique. This is the first result which proves uniqueness when the velocity is far from Lipschitz and the initial vorticity is non-constant around the boundary.