×

Global existence and convergence rates for the 3-D compressible Navier-Stokes equations without heat conductivity. (English) Zbl 1166.35029

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.

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
PDFBibTeX XMLCite
Full Text: DOI