Global existence for a one-dimensional model in gas dynamics

Serge Njamkepo

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 2, page 203-221
  • ISSN: 1233-7234

Abstract

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We prove the existence of a global solution for a one-dimensio- nal Navier-Stokes system for a gas with internal capillarity.

How to cite

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Njamkepo, Serge. "Global existence for a one-dimensional model in gas dynamics." Applicationes Mathematicae 24.2 (1997): 203-221. <http://eudml.org/doc/219163>.

@article{Njamkepo1997,
abstract = {We prove the existence of a global solution for a one-dimensio- nal Navier-Stokes system for a gas with internal capillarity.},
author = {Njamkepo, Serge},
journal = {Applicationes Mathematicae},
keywords = {capillarity; Navier-Stokes equations; gas dynamics; adiabatic flow of viscous gas; iterative procedure; local existence; second gradient theory; internal capillarity; fourth-order viscosity coefficient; uniform Gronwall lemma},
language = {eng},
number = {2},
pages = {203-221},
title = {Global existence for a one-dimensional model in gas dynamics},
url = {http://eudml.org/doc/219163},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Njamkepo, Serge
TI - Global existence for a one-dimensional model in gas dynamics
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 2
SP - 203
EP - 221
AB - We prove the existence of a global solution for a one-dimensio- nal Navier-Stokes system for a gas with internal capillarity.
LA - eng
KW - capillarity; Navier-Stokes equations; gas dynamics; adiabatic flow of viscous gas; iterative procedure; local existence; second gradient theory; internal capillarity; fourth-order viscosity coefficient; uniform Gronwall lemma
UR - http://eudml.org/doc/219163
ER -

References

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  4. [Ga-S] R. Gatignol and P. Seppecher, Modelisation of fluid-fluid interfaces with material properties, J. Méc. Théor. Appl. 1986, 225-247. Zbl0613.76116
  5. [G] P. Germain, La méthode des puissances virtuelles en mécanique des milieux continus, J. Mécanique 12 (1973), 235-274. Zbl0261.73003
  6. [G-T] J.-M. Ghidaglia and R. Temam, Long time behavior for partly dissipative equations: the slightly compressible 2D-Navier-Stokes equations, Asymptotic Anal. 1 (1988), 23-49. Zbl0657.76029
  7. [K-S] A. V. Kazhikhov and S. Shelukin, Unique solution with respect to time of initial boundary value problem for one dimensional equations of a viscous gas, J. Appl. Math. Mech. 4 (1982), 273-282. 
  8. [M-N] A. Matsumura and A. Nishida, The initial value problem for the equations of motion of viscous and heat conductive gases, J. Math. Kyoto Univ. 20 (1980), 67-104. Zbl0429.76040
  9. [S] P. Seppecher, Etude d'une modélisation des zones capillaires fluides: interfaces et lignes de contact, Thèse de Doctorat, Université Paris VI, 1987. 
  10. [Se1] D. Serre, Sur l'équation monodimensionnelle d'un fluide visqueux compressible et conducteur de chaleur, C. R. Acad. Sci. Paris Sér. I 303 (1986), 703-706. Zbl0611.35070
  11. [Se2] D. Serre, Solutions faibles globales des équations de Navier-Stokes pour un fluide compressible, ibid., 639-642. Zbl0597.76067
  12. [Se3] D. Serre, Entropie du mélange liquide-vapeur d'un fluide thermo-capillaire, Arch. Rationel Mech. Anal. 128 (1994), 33-73. 

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