Vanishing viscosity in the plane for nondecaying velocity and vorticity

TL;DR

This paper demonstrates that, under bounded initial conditions, solutions of the Navier-Stokes equations in the plane converge uniformly to Euler solutions as viscosity tends to zero, with an established rate of convergence.

Contribution

It proves uniform convergence of Navier-Stokes solutions to Euler solutions in the plane for bounded initial velocity and vorticity, including a convergence rate.

Findings

Uniform convergence on short time intervals

Convergence rate of solutions as viscosity vanishes

Unique solutions for both Navier-Stokes and Euler equations

Abstract

Assuming that initial velocity and initial vorticity are bounded in the plane, we show that on a sufficiently short 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.