Global solutions to the Lagrangian averaged Navier-Stokes equation in low regularity Besov spaces. (English) Zbl 1254.76057

Summary: 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 \(p>n\).


76D05 Navier-Stokes equations for incompressible viscous fluids
35K58 Semilinear parabolic equations
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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