Lagrangian Averaged Navier-Stokes equations with rough data in Sobolev space

TL;DR

This paper establishes the existence of short-time solutions with low regularity for the Lagrangian Averaged Navier-Stokes equations and extends global existence results for specific Sobolev initial data.

Contribution

It proves the existence of low regularity solutions and improves global existence results for initial data in certain Sobolev spaces.

Findings

Existence of short-time solutions for low regularity data

Global solutions for initial data in $H^{3/2,2}(\

Abstract

We prove the existence of short time, low regularity solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equations with initial data in Sobolev spaces. In the special case of initial datum in the Sobolev space $H^{3/2,2}(\mathbb{R}^3)$, we obtain a global solution, improving on previous results, which required data in $H^{3,2}(\mathbb{R}^3)$.