JournalszaaVol. 28 , No. 1DOI 10.4171/zaa/1370

Global Smooth Solutions of Viscous Compressible Real Flows with Density-Dependent Viscosity

  • Xulong Qin

    Sun Yat-Sen University, Guangzhou, China
  • Zheng-an Yao

    Sun Yat-Sen University, Guangzhou, China
Global Smooth Solutions of Viscous Compressible Real Flows with Density-Dependent Viscosity cover

Abstract

We consider an initial boundary problem of viscous, compressible, heat-conducting real fluids with density-dependent viscosity. More precisely, we assume that the viscosity μ(ρ)=ρλ\mu(\rho)=\rho^{\lambda}, where ρ\rho is the density of flows and λ\lambda is a positive constant. The equations of state for the real flows depend nonlinearly upon the temperature and the density unlike the linear dependence for the perfect flows. We prove the global existence (uniqueness) of smooth solutions under the hypotheses: λ(2(γ1),12]\lambda \in \big(2(\gamma-1),\frac12\big] and 1γ<541\leq \gamma <\frac54 , which improves a previous result. In particular, we also show that no vacuum will be developed provided the initial density is far away from vacuum.