TY - JOUR
T1 - On some compressible fluid models
T2 - Korteweg, lubrication, and shallow water systems
AU - Bresch, Didier
AU - Desjardins, Benoît
AU - Lin, Chi Kun
N1 - Funding Information:
This work has been written during the stay of the first two authors in Taiwan in April 2002. Their research was supported by the National Center for Theoretical Sciences in Hsinchu, Taiwan. Chi-Kun Lin is also partially supported by NSC90-2115-M006-026. D. Bresch and B. Desjardins want to thank the Taiwanese for their hospitality.
PY - 2003
Y1 - 2003
N2 - In this article, we give some mathematical results for an isothermal model of capillary compressible fluids derived by Dunn and Serrin in (Dunn JE, Serrin J. On the thermodynamics of interstitial working. Arch Rational Mech Anal. 1985; 88(2):95-133), which can be used as a phase transition model. We consider a periodic domain Ω = Td (d = 2 ou 3) or a strip domain Ω = (0,1) × Td-1. We look at the dependence of the viscosity μ and the capillarity coefficient κ with respect to the density ρ. Depending on the cases we consider, different results are obtained. We prove for instance for a viscosity μ(ρ)-νρ and a surface tension κ(ρ) = κ̃ = cte the global existence of weak solutions of the Korteweg system without smallness assumption on the data. This model includes a shallow water model and a lubrication model. We discuss the validity of the result for the shallow water equations since the density is less regular than in the Korteweg case.
AB - In this article, we give some mathematical results for an isothermal model of capillary compressible fluids derived by Dunn and Serrin in (Dunn JE, Serrin J. On the thermodynamics of interstitial working. Arch Rational Mech Anal. 1985; 88(2):95-133), which can be used as a phase transition model. We consider a periodic domain Ω = Td (d = 2 ou 3) or a strip domain Ω = (0,1) × Td-1. We look at the dependence of the viscosity μ and the capillarity coefficient κ with respect to the density ρ. Depending on the cases we consider, different results are obtained. We prove for instance for a viscosity μ(ρ)-νρ and a surface tension κ(ρ) = κ̃ = cte the global existence of weak solutions of the Korteweg system without smallness assumption on the data. This model includes a shallow water model and a lubrication model. We discuss the validity of the result for the shallow water equations since the density is less regular than in the Korteweg case.
UR - http://www.scopus.com/inward/record.url?scp=0038174797&partnerID=8YFLogxK
U2 - 10.1081/PDE-120020499
DO - 10.1081/PDE-120020499
M3 - Article
AN - SCOPUS:0038174797
SN - 0360-5302
VL - 28
SP - 843
EP - 868
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 3-4
ER -