  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 $H^{3,2}(\mathbb{R}^3)$.
