Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces

Nathan Pennington

Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces

Research output: Contribution to journal › Article › peer-review

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(R³) and in the Besov space B^n/2 _2,q (Rⁿ). 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 (R³) for any p > n.

Original language	English (US)
Pages (from-to)	697-724
Number of pages	28
Journal	Advances in Differential Equations
Volume	17
Issue number	7-8
State	Published - 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Cite this

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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 H3/4,2(R3) and in the Besov space Bn/2 2,q (Rn). In this paper, we use an interpolation-based method to prove the existence of global solutions to the LANS equation with initial data in B3/p p,q (R3) for any p > n.",

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Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces

Abstract

All Science Journal Classification (ASJC) codes

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