## Differential and Integral Equations

### Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations

Benoit Desjardins

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 10, Number 3 (1997), 577-586.

Dates
First available in Project Euclid: 2 May 2013