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

Sébastien Novo and Antonin Novotný

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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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250283849

Digital Object Identifier
doi:10.1215/kjm/1250283849

Mathematical Reviews number (MathSciNet)
MR1967222

Zentralblatt MATH identifier
1050.35074

Subjects
Primary: 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]
Secondary: 35D05 35Q35: PDEs in connection with fluid mechanics

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


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