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1997 Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations
Benoit Desjardins
Differential Integral Equations 10(3): 577-586 (1997).

Abstract

The purpose of this note is to present new results on linear transport equations with initial values in $W^{1,r}(\Omega)$ spaces, and coefficients in $W^{s+1,p}(\Omega)^N$, where $\Omega$ is a bounded open subset of $\mathbb{R}^N$ ($N \geq 2$) and $sp=N$. As an application, we also give refined regularity and uniqueness results for weak solutions of the two-dimensional density-dependent incompressible Navier-Stokes equations.

Citation

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Benoit Desjardins. "Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations." Differential Integral Equations 10 (3) 577 - 586, 1997.

Information

Published: 1997
First available in Project Euclid: 2 May 2013

zbMATH: 0902.76028
MathSciNet: MR1744862

Subjects:
Primary: 35Q30
Secondary: 76D03, 76D05

Rights: Copyright © 1997 Khayyam Publishing, Inc.

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Vol.10 • No. 3 • 1997
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