Dissipative continuous Euler flows in two and three dimensions

Abstract

Recently, two of these authors construct dissipative continuous (weak) solutions to the incompressible Euler equations on the three-dimensional torus ${\mathbb{T}}^3$. The building blocks in their proof are Beltrami flows, which are inherently three-dimensional. The purpose of this note is to show that the techniques can nevertheless be adapted to the two-dimensional case.

29 pages

References in corpus (1)

• On admissibility criteria for weak solutions of the Euler equations

Cited by in corpus (7)

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• The Euler Equations in planar nonsmooth convex domains
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• Cauchy problem for dissipative Hölder solutions to the incompressible Euler equations
• Holder Continuous Solutions of Active Scalar Equations
• Hölder Continuous Solutions Of Boussinesq Equation with compact support
• Non-uniqueness of weak solutions to 2D hypoviscous Navier-Stokes equations