On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable
Feireisl, Eduard
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 83-98 / Harvested from Czech Digital Mathematics Library
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We show compactness of bounded sets of weak solutions to the isentropic compressible Navier-Stokes equations in three space dimensions under the hypothesis that the adiabatic constant $\gamma >3/2$.

Publié le : 2001-01-01
Classification:  35B05,  35Q30,  76N10 
@article{119225,
     author = {Eduard Feireisl},
     title = {On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {83-98},
     zbl = {1115.35096},
     mrnumber = {1825374},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119225}
}

Feireisl, Eduard. On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 83-98. http://gdmltest.u-ga.fr/item/119225/

Bogovskii M.E. Solution of some vector analysis problems connected with operators div and grad (in Russian), Trudy Sem. S.L. Sobolev 80(1) 5-40 (1980). (1980) | MR 0631691

Borchers W.; Sohr H. On the equation $rot v = g$ and $div u = f$ with zero boundary conditions, Hokkaido Math. J. 19 67-87 (1990). (1990) | MR 1039466

Diperna R.J.; Lions P.-L. Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 511-547 (1989). (1989) | MR 1022305 | Zbl 0696.34049

Feireisl E.; Matušů-Nečasová Š.; Petzeltová H.; Straškraba I. On the motion of a viscous compressible flow driven by a time-periodic external flow, Arch. Rational Mech. Anal. 149 69-96 (1999). (1999) | MR 1723036

Feireisl E.; Petzeltová H. On compactness of solutions to the Navier-Stokes equations of compressible flow, J. Differential Equations 163(1) 57-75 (2000). (2000) | MR 1755068

Feireisl E.; Petzeltová H. On integrability up to the boundary of the weak solutions of the Navier-Stokes equations of compressible flow, Commun. Partial Differential Equations 25(3-4) 755-767 (2000). (2000) | MR 1748351

Galdi G.P. An Introduction to the Mathematical Theory of the Navier-Stokes Equations, I., Springer-Verlag, New York, 1994.

Jiang S.; Zhang P. On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations, preprint, 1999. | MR 1810944 | Zbl 0980.35126

Lions P.-L. Mathematical Topics in Fluid Dynamics, Vol.2, Compressible Models, Oxford Science Publication, Oxford, 1998. | MR 1637634

Lions P.-L. Bornes sur la densité pour les équations de Navier-Stokes compressible isentropiques avec conditions aux limites de Dirichlet, C.R. Acad. Sci. Paris, Sér I. 328 659-662 (1999). (1999) | MR 1680813

Yi Z. An $L^p$ theorem for compensated compactness, Proc. Royal Soc. Edinburgh 122A (1992), 177-189. (1992) | MR 1190238 | Zbl 0848.32025