Existence of strong solutions for nonisothermal Korteweg system

Boris Haspot[1]

  • [1] Université Paris-Est Laboratoire d’Analyse et de Mathématiques Appliquées, UMR 8050 61 avenue du Général de Gaulle 94 010 CRETEIL Cedex FRANCE

Annales mathématiques Blaise Pascal (2009)

  • Volume: 16, Issue: 2, page 431-481
  • ISSN: 1259-1734

Abstract

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This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J. E Dunn and J. Serrin (1985) in [9, 16], which can be used as a phase transition model.We distinguish two cases, when the physical coefficients depend only on the density, and the general case. In the first case we can work in critical scaling spaces, and we prove global existence of solution and uniqueness for data close to a stable equilibrium. For general data, existence and uniqueness is stated on a short time interval.In the general case with physical coefficients depending on density and on temperature, additional regularity is required to control the temperature in L ∞ norm. We prove global existence of solution close to a stable equilibrium and local in time existence of solution with more general data. Uniqueness is also obtained.

How to cite

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Haspot, Boris. "Existence of strong solutions for nonisothermal Korteweg system." Annales mathématiques Blaise Pascal 16.2 (2009): 431-481. <http://eudml.org/doc/10587>.

@article{Haspot2009,
abstract = {This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J. E Dunn and J. Serrin (1985) in [9, 16], which can be used as a phase transition model.We distinguish two cases, when the physical coefficients depend only on the density, and the general case. In the first case we can work in critical scaling spaces, and we prove global existence of solution and uniqueness for data close to a stable equilibrium. For general data, existence and uniqueness is stated on a short time interval.In the general case with physical coefficients depending on density and on temperature, additional regularity is required to control the temperature in $L^\{\infty \}$ norm. We prove global existence of solution close to a stable equilibrium and local in time existence of solution with more general data. Uniqueness is also obtained.},
affiliation = {Université Paris-Est Laboratoire d’Analyse et de Mathématiques Appliquées, UMR 8050 61 avenue du Général de Gaulle 94 010 CRETEIL Cedex FRANCE},
author = {Haspot, Boris},
journal = {Annales mathématiques Blaise Pascal},
keywords = {PDE; Harmonic analysis; initial boundary value problem; general non-isothermal model of capillary fluids; phase transition model},
language = {eng},
month = {7},
number = {2},
pages = {431-481},
publisher = {Annales mathématiques Blaise Pascal},
title = {Existence of strong solutions for nonisothermal Korteweg system},
url = {http://eudml.org/doc/10587},
volume = {16},
year = {2009},
}

TY - JOUR
AU - Haspot, Boris
TI - Existence of strong solutions for nonisothermal Korteweg system
JO - Annales mathématiques Blaise Pascal
DA - 2009/7//
PB - Annales mathématiques Blaise Pascal
VL - 16
IS - 2
SP - 431
EP - 481
AB - This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J. E Dunn and J. Serrin (1985) in [9, 16], which can be used as a phase transition model.We distinguish two cases, when the physical coefficients depend only on the density, and the general case. In the first case we can work in critical scaling spaces, and we prove global existence of solution and uniqueness for data close to a stable equilibrium. For general data, existence and uniqueness is stated on a short time interval.In the general case with physical coefficients depending on density and on temperature, additional regularity is required to control the temperature in $L^{\infty }$ norm. We prove global existence of solution close to a stable equilibrium and local in time existence of solution with more general data. Uniqueness is also obtained.
LA - eng
KW - PDE; Harmonic analysis; initial boundary value problem; general non-isothermal model of capillary fluids; phase transition model
UR - http://eudml.org/doc/10587
ER -

References

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