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.
Citation
Sébastien Novo. Antonin Novotný. "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 (3) 531 - 550, 2002. https://doi.org/10.1215/kjm/1250283849
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