## Journal of Mathematics of Kyoto University

### On the existence of weak solutions to the steady compressible Navier-Stokes equations when the density is not square integrable

#### Abstract

We consider the steady compressible Navier-Stokes equations in the isentropic regime in a bounded domain of $\mathbb{R}^{3}$. We show that the renormalized continuity equation holds even if the density is not square integrable. We use this result to prove existence of weak solutions under the sole hypothesis $\gamma > 3/2$ for the adiabatic constant.

#### Article information

Source
J. Math. Kyoto Univ., Volume 42, Number 3 (2002), 531-550.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250283849

Digital Object Identifier
doi:10.1215/kjm/1250283849

Mathematical Reviews number (MathSciNet)
MR1967222

Zentralblatt MATH identifier
1050.35074

#### Citation

Novo, Sébastien; Novotný, Antonin. On the existence of weak solutions to the steady compressible Navier-Stokes equations when the density is not square integrable. J. Math. Kyoto Univ. 42 (2002), no. 3, 531--550. doi:10.1215/kjm/1250283849. https://projecteuclid.org/euclid.kjm/1250283849