A finite time result for vanishing viscosity in the plane with nondecaying vorticity

TL;DR

This paper proves that solutions of the Navier-Stokes equations with bounded vorticity in the plane converge uniformly to Euler solutions as viscosity tends to zero, providing a finite-time convergence rate.

Contribution

It establishes a finite-time convergence result for vanishing viscosity in 2D with bounded vorticity, including a quantitative rate of convergence.

Findings

Solutions of Navier-Stokes converge uniformly to Euler solutions as viscosity approaches zero.

Convergence holds for any finite time interval.

A rate of convergence is explicitly established.

Abstract

Assuming that initial velocity has finite energy and initial vorticity is bounded in the plane, we show that for any finite time interval the unique solutions of the Navier-Stokes equations converge uniformly to the unique solution of the Euler equations as viscosity approaches zero. We also establish a rate of convergence.