Lagrangian Averaged Navier-Stokes equations with rough data in Sobolev space

Details Lagrangian Averaged Navier-Stokes equations with rough data in Sobolev space Lagrangian Averaged Navier-Stokes equations with rough data in Sobolev space

2010-11-08

arxiv.org/abs/1011.1856v2

Mathematics

Analysis of PDEs

Scientific paper

We prove the existence of short time, low regularity solutions to the
incompressible, isotropic Lagrangian Averaged Navier-Stokes equations with
initial data in Sobolev spaces. In the special case of initial datum in the
Sobolev space $H^{3/2,2}(\mathbb{R}^3)$, we obtain a global solution, improving
on previous results, which required data in $H^{3,2}(\mathbb{R}^3)$.

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