Local Well-Posedness Of The Anisotropic Lagrangian Averaged Navier-Stokes Equations With Stokes Projector Viscosity

The anisotropic Lagrangian averaged Navier-Stokes (LANS-alpha) equations are a coupled system of nonlinear partial differential equations designed to capture both the large scale motion of an incompressible fluid and the covariance tensor. There are two choices for the divergence-free projection of the viscosity term. One choice is the classical L-2 -orthogonal Leray projector. In this case, Marsden and Shkoller (2003) show that strong solutions exist and are unique in the three-dimensional periodic box for a finite time interval. We extend this result by considering the second choice of projector, the generalized Stokes projector.