On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity

Abstract

We show strong convergence of the vorticities in the vanishing viscosity limit for the incompressible Navier-Stokes equations on the two-dimensional torus, assuming only that the initial vorticity of the limiting Euler equations is in $L^p$ for some $p>1$. This substantially extends a recent result of Constantin, Drivas and Elgindi, who proved strong convergence in the case $p=\infty$. Our proof, which relies on the classical renormalization theory of DiPerna-Lions, is surprisingly simple.

arXiv commentThe statement of the main theorem has been improved

References in corpus (4)

• Lagrangian flows for vector fields with gradient given by a singular integral
• A quantitative theory for the continuity equation
• Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid. Part I
• A note on the vanishing viscosity limit in the Yudovich class

Cited by in corpus (6)

• Statistical solutions of the incompressible Euler equations
• Probabilistic Descriptions of Fluid Flow: A Survey
• Energy balance for forced two-dimensional incompressible ideal fluid flow
• Existence of weak solutions to the two-dimensional incompressible Euler equations in the presence of sources and sinks
• On Maximum Enstrophy Dissipation in 2D Navier-Stokes Flows in the Limit of Vanishing Viscosity
• Energy conservation for 2D Euler with vorticity in $L(\log L{)}^{\alpha }$