On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable

Eduard Feireisl

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 1, page 83-98
  • ISSN: 0010-2628

Abstract

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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 γ > 3 / 2 .

How to cite

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Feireisl, Eduard. "On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable." Commentationes Mathematicae Universitatis Carolinae 42.1 (2001): 83-98. <http://eudml.org/doc/248795>.

@article{Feireisl2001,
abstract = {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 $\gamma >3/2$.},
author = {Feireisl, Eduard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compressible flow; weak solutions; compactness; compressible flow; weak solutions; compactness; compressible isentropic Navier-Stokes equations},
language = {eng},
number = {1},
pages = {83-98},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable},
url = {http://eudml.org/doc/248795},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Feireisl, Eduard
TI - On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 1
SP - 83
EP - 98
AB - 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 $\gamma >3/2$.
LA - eng
KW - compressible flow; weak solutions; compactness; compressible flow; weak solutions; compactness; compressible isentropic Navier-Stokes equations
UR - http://eudml.org/doc/248795
ER -

References

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  3. DiPerna R.J., Lions P.-L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 511-547 (1989). (1989) Zbl0696.34049MR1022305
  4. 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) MR1723036
  5. 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) MR1755068
  6. 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) MR1748351
  7. Galdi G.P., An Introduction to the Mathematical Theory of the Navier-Stokes Equations, I., Springer-Verlag, New York, 1994. 
  8. Jiang S., Zhang P., On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations, preprint, 1999. Zbl0980.35126MR1810944
  9. Lions P.-L., Mathematical Topics in Fluid Dynamics, Vol.2, Compressible Models, Oxford Science Publication, Oxford, 1998. MR1637634
  10. 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) MR1680813
  11. Yi Z., An L p theorem for compensated compactness, Proc. Royal Soc. Edinburgh 122A (1992), 177-189. (1992) Zbl0848.32025MR1190238

Citations in EuDML Documents

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  1. Vincent Girinon, Navier-Stokes equations with nonhomogeneous boundary conditions in a convex bi-dimensional domain
  2. Vít Dolejší, Miloslav Feistauer, Jiří Felcman, Výpočtová matematika a počítačová dynamika tekutin
  3. Jens Frehse, Sonja Goj, Josef Málek, A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum
  4. Eduard Feireisl, On the motion of rigid bodies in a viscous fluid
  5. Eduard Feireisl, Some recent results on the existence of global-in-time weak solutions to the Navier-Stokes equations of a general barotropic fluid
  6. Nader Masmoudi, Homogenization of the compressible Navier–Stokes equations in a porous medium
  7. Nader Masmoudi, Homogenization of the compressible Navier–Stokes equations in a porous medium
  8. Jan Březina, Antonín Novotný, On weak solutions of steady Navier-Stokes equations for monatomic gas

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