Blow up for the 2D Euler Equation on Some Bounded Domains

2014/06/13 by Kiselev, Alexander, Zlatos, Andrej
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1406.3648

Abstract

We find a smooth solution of the 2D Euler equation on a bounded domain which exists and is unique in a natural class locally in time, but blows up in finite time in the sense of its vorticity losing continuity. The domain's boundary is smooth except at two points, which are interior cusps.

Related

• The 2D Euler equation on singular domains
• Wellposedness and singularity formation beyond the Yudovich class
• Vorticity blowup in 2D compressible Euler equations
• Velocity blow-up in C¹∩ H² for the 2D Euler equations
• Uniqueness of the 2D Euler equation on a corner domain with non-constant vorticity around the corner