Duan, Renjun; Ma, Hongfang Global existence and convergence rates for the 3-D compressible Navier-Stokes equations without heat conductivity. (English) Zbl 1166.35029 Indiana Univ. Math. J. 57, No. 5, 2299-2319 (2008). Summary: We study the global existence and convergence rates of solutions to the three-dimensional compressible Navier-Stokes equations without heat conductivity, which is a hyperbolic-parabolic system. The pressure and velocity are dissipative because of the viscosity, whereas the entropy is non-dissipative due to the absence of heat conductivity. The global solutions are obtained by combining the local existence and a priori estimates if the \(H^3\)-norm of the initial perturbation around a constant state is small enough and its \(L^1\)-norm is bounded. A priori decay-in-time estimates on the pressure and velocity are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained. Cited in 4 ReviewsCited in 41 Documents MSC: 35Q30 Navier-Stokes equations 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 93D20 Asymptotic stability in control theory 34B45 Boundary value problems on graphs and networks for ordinary differential equations Keywords:Navier-Stokes equations; a priori estimate; convergence rates PDFBibTeX XMLCite \textit{R. Duan} and \textit{H. Ma}, Indiana Univ. Math. J. 57, No. 5, 2299--2319 (2008; Zbl 1166.35029) Full Text: DOI