Some remarks to the compactness of steady compressible isentropic Navier-Stokes equations via the decomposition method

Antonín Novotný

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 2, page 305-342
  • ISSN: 0010-2628

Abstract

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In [18]–[19], P.L. Lions studied (among others) the compactness and regularity of weak solutions to steady compressible Navier-Stokes equations in the isentropic regime with arbitrary large external data, in particular, in bounded domains. Here we investigate the same problem, combining his ideas with the method of decomposition proposed by Padula and myself in [29]. We find the compactness of the incompressible part u of the velocity field v and we give a new proof of the compactness of the “effective pressure” 𝒫 = ρ γ - ( 2 μ 1 + μ 2 ) div v . We derive some new estimates of these quantities in Hardy and Triebel-Lizorkin spaces.

How to cite

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Novotný, Antonín. "Some remarks to the compactness of steady compressible isentropic Navier-Stokes equations via the decomposition method." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 305-342. <http://eudml.org/doc/247928>.

@article{Novotný1996,
abstract = {In [18]–[19], P.L. Lions studied (among others) the compactness and regularity of weak solutions to steady compressible Navier-Stokes equations in the isentropic regime with arbitrary large external data, in particular, in bounded domains. Here we investigate the same problem, combining his ideas with the method of decomposition proposed by Padula and myself in [29]. We find the compactness of the incompressible part $u$ of the velocity field $v$ and we give a new proof of the compactness of the “effective pressure” $\{\mathcal \{P\}\} = \rho ^\gamma - (2\mu _1 +\mu _2) \operatorname\{div\} v$. We derive some new estimates of these quantities in Hardy and Triebel-Lizorkin spaces.},
author = {Novotný, Antonín},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {steady compressible Navier-Stokes equations; Poisson-Stokes equations; weak solutions; global existence of weak solutions; div-curl lemma; Hardy spaces; Triebel-Lizorkin spaces; Poisson-Stokes equations; weak solutions; global existence of weak solutions; div-curl lemma; Hardy spaces; Triebel-Lizorkin spaces},
language = {eng},
number = {2},
pages = {305-342},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some remarks to the compactness of steady compressible isentropic Navier-Stokes equations via the decomposition method},
url = {http://eudml.org/doc/247928},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Novotný, Antonín
TI - Some remarks to the compactness of steady compressible isentropic Navier-Stokes equations via the decomposition method
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 305
EP - 342
AB - In [18]–[19], P.L. Lions studied (among others) the compactness and regularity of weak solutions to steady compressible Navier-Stokes equations in the isentropic regime with arbitrary large external data, in particular, in bounded domains. Here we investigate the same problem, combining his ideas with the method of decomposition proposed by Padula and myself in [29]. We find the compactness of the incompressible part $u$ of the velocity field $v$ and we give a new proof of the compactness of the “effective pressure” ${\mathcal {P}} = \rho ^\gamma - (2\mu _1 +\mu _2) \operatorname{div} v$. We derive some new estimates of these quantities in Hardy and Triebel-Lizorkin spaces.
LA - eng
KW - steady compressible Navier-Stokes equations; Poisson-Stokes equations; weak solutions; global existence of weak solutions; div-curl lemma; Hardy spaces; Triebel-Lizorkin spaces; Poisson-Stokes equations; weak solutions; global existence of weak solutions; div-curl lemma; Hardy spaces; Triebel-Lizorkin spaces
UR - http://eudml.org/doc/247928
ER -

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