Decay of the Compressible Navier-Stokes Equations with Hyperbolic Heat Conduction

Compressible Navier-Stokes equations with hyperbolic heat conduction

In this paper, we investigate the system of compressible Navier-Stokes equations with hyperbolic heat conduction, i.e., replacing the Fourier’s law by Cattaneo’s law. First, by using Kawashima’s condition on general hyperbolic parabolic systems, we show that for small relaxation time τ , global smooth solution exists for small initial data. Moreover, as τ goes to zero, we obtain the uniform con...

Compressible Navier-stokes Equations with Temperature Dependent Heat Conductivities

We prove the existence and uniqueness of global strong solutions to the one dimensional, compressible Navier-Stokes system for the viscous and heat conducting ideal polytropic gas flow, when heat conductivity depends on temperature in power law of Chapman-Enskog. The results reported in this article is valid for initial boundary value problem with non-slip and heat insulated boundary along with...

On the barotropic compressible Navier-Stokes equations

We consider barotropic compressible Navier-Stokes equations with density dependent viscosity coefficients that vanish on vacuum. We prove the stability of weak solutions in periodic domain Ω = T and in the whole space Ω = R , when N = 2 and N = 3. The pressure is given by p(ρ) = ρ and our result holds for any γ > 1. Note that our notion of weak solutions is not the usual one. In particular we r...

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

Decay rate of the compressible Navier-Stokes equations with density-dependent viscosity coefficients