The Lagrangian Averaged Navier-Stokes (LANS) equations are a recently derived approximation to the Navier-Stokes equations. Existence of global solutions for the LANS equation has been proven for initial data in the Sobolev space $H^{ 3/4,2}(\mathbb{ R}^3)$ and in the Besov space $B^{ 3/2}_{ 2,q}(\mathbb{ R}^3)$. In this paper, we use an interpolation based method to prove the existence of global solutions to the LANS equation with initial data in $B^{ 3/p}_{ p,q}(\mathbb{ R}^3)$ for any $p>3$.
Categories: math.AP