Some recent results on the existence of global-in-time weak solutions to the Navier-Stokes equations of a general barotropic fluid

Eduard Feireisl

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 203-209
  • ISSN: 0862-7959

Abstract

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This is a survey of some recent results on the existence of globally defined weak solutions to the Navier-Stokes equations of a viscous compressible fluid with a general barotropic pressure-density relation.

How to cite

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Feireisl, Eduard. "Some recent results on the existence of global-in-time weak solutions to the Navier-Stokes equations of a general barotropic fluid." Mathematica Bohemica 127.2 (2002): 203-209. <http://eudml.org/doc/249037>.

@article{Feireisl2002,
abstract = {This is a survey of some recent results on the existence of globally defined weak solutions to the Navier-Stokes equations of a viscous compressible fluid with a general barotropic pressure-density relation.},
author = {Feireisl, Eduard},
journal = {Mathematica Bohemica},
keywords = {compressible Navier-Stokes equations; global existence; weak solutions; global existence; weak solutions; Navier-Stokes equations; viscous compressible fluid},
language = {eng},
number = {2},
pages = {203-209},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some recent results on the existence of global-in-time weak solutions to the Navier-Stokes equations of a general barotropic fluid},
url = {http://eudml.org/doc/249037},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Some recent results on the existence of global-in-time weak solutions to the Navier-Stokes equations of a general barotropic fluid
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 203
EP - 209
AB - This is a survey of some recent results on the existence of globally defined weak solutions to the Navier-Stokes equations of a viscous compressible fluid with a general barotropic pressure-density relation.
LA - eng
KW - compressible Navier-Stokes equations; global existence; weak solutions; global existence; weak solutions; Navier-Stokes equations; viscous compressible fluid
UR - http://eudml.org/doc/249037
ER -

References

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  1. Boundary Value Problems of Mechanics of Non-Homogeneous Fluids, Novosibirsk, 1983. (Russian) (1983) 
  2. 10.1007/BF01393835, Invent. Math. 98 (1989), 511–547. (1989) MR1022305DOI10.1007/BF01393835
  3. Global in time weak solutions for compressible barotropic self-gravitating fluids, Adv. Appl. Math. Submitted (2001). (2001) MR1841897
  4. The dynamical systems approach to the Navier-Stokes equations of compressible fluid, Advances in Mathematical Fluid Mechanics, J. Málek, J. Nečas, M. Rokyta (eds.), Springer, Berlin, 2000. (2000) MR1863209
  5. On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable, Comment. Math. Univ. Carolin. 42 (2001), 83–98. (2001) Zbl1115.35096MR1825374
  6. On the domain dependence of solutions to the compressible Navier-Stokes equations of a barotropic fluid, Math. Meth. Appl. Sci (to appear). (to appear) MR1918742
  7. On the existence of globally defined weak solutions to the Navier-Stokes equations of compressible isentropic fluids, J. Math. Fluid Dynamics 3 (2001), 358–392. (2001) MR1867887
  8. 10.1080/03605300008821530, Commun. Partial Differential Equations 25 (2000), 755–767. (2000) MR1748351DOI10.1080/03605300008821530
  9. Mathematical Topics in Fluid Dynamics, Vol. 2, Compressible Models, Oxford Science Publication, Oxford, 1998. (1998) MR1637634
  10. 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 (1999), 659–662. (1999) MR1680813

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