On the existence of weak solutions to the steady compressible Navier-Stokes equations when the density is not square integrable
Novo, Sébastien ; Novotný, Antonin
J. Math. Kyoto Univ., Tome 42 (2002) no. 4, p. 531-550 / Harvested from Project Euclid
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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.
Publié le : 2002-05-15
Classification:  76N10,  35D05,  35Q35 
@article{1250283849,
     author = {Novo, S\'ebastien and Novotn\'y, Antonin},
     title = {On the existence of weak solutions to the steady compressible Navier-Stokes equations when the density is not square integrable},
     journal = {J. Math. Kyoto Univ.},
     volume = {42},
     number = {4},
     year = {2002},
     pages = { 531-550},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250283849}
}

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., Tome 42 (2002) no. 4, pp.  531-550. http://gdmltest.u-ga.fr/item/1250283849/