Advances in Differential Equations

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

Nathan Pennington

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 $B^{n/2}_{2,q}(\mathbb{R}^n)$. 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 $p>n$.

Article information

Source
Adv. Differential Equations, Volume 17, Number 7/8 (2012), 697-724.

Dates
First available in Project Euclid: 17 December 2012

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