The Lagrangian Averaged Navier-Stokes equation with rough data in Sobolev spaces

The Lagrangian Averaged Navier-Stokes equation is a recently derived approximation to the Navier-Stokes equation. In this article we prove the existence of short time solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equation with low regularity initial data in Sobolev spaces Ws,p(Rn) for 1