On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids

Piotr Boguslaw Mucha; Wojciech Zajączkowski

Piotr Boguslaw Mucha ; Wojciech Zajączkowski

Annales Polonici Mathematici, Tome 79 (2002), p. 227-239 / Harvested from The Polish Digital Mathematics Library

Résumé

The local existence of solutions for the compressible Navier-Stokes equations with the Dirichlet boundary conditions in the $L_{p}$ -framework is proved. Next an almost-global-in-time existence of small solutions is shown. The considerations are made in Lagrangian coordinates. The result is sharp in the $L_{p}$ -approach, because the velocity belongs to $W_{r}^{2, 1}$ with r > 3.

Publié le : 2002-01-01

Zbl 0992.35063

EUDML-ID : urn:eudml:doc:280610

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     title = {On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids},
     journal = {Annales Polonici Mathematici},
     volume = {79},
     year = {2002},
     pages = {227-239},
     zbl = {0992.35063},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-3-2}
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Piotr Boguslaw Mucha; Wojciech Zajączkowski. On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids. Annales Polonici Mathematici, Tome 79 (2002) pp. 227-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-3-2/