Global Solutions to the Lagrangian Averaged Navier-Stokes equation in low regularity Besov spaces

Abstract

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 $B_{2,q}^{3/2}({\mathbb{R}}^3)$. In this paper, we use an interpolation based method to prove the existence of global solutions to the LANS equation with initial data in $B_{p,q}^{3/p}({\mathbb{R}}^3)$ for any $p>3$.

References in corpus (1)

• On Incompressible Averaged Lagrangian Hydrodynamics