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

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

2011-10-21

arxiv.org/abs/1110.4668v2

Mathematics

Analysis of PDEs

Scientific paper

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 $p>3$.

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