Symmetric Compressible Navier-Stokes Equations Research Articles

Global strong solutions to radial symmetric compressible Navier–Stokes equations bounded by a free surface

ABSTRACTIn this paper, we consider the two-dimensional isentropic compressible Navier–Stokes equations bounded by a free surface that is under the surface tension and constant exterior pressure. We establish the existence of global strong solution for arbitrary large spherical initial data with initial density away from the vacuum in the case the viscosity coefficients satisfy . In particular, we show that the density is strictly positive and bounded from the above and below in any finite time if the initial density is strictly positive.

Global Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data

We consider the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data in this paper. For piecewise regular initial density with bounded jump discontinuity, we show that there exists a unique global piecewise regular solution. In particular, the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially ast→+∞.

Global solution to the exterior problem for spherically symmetric compressible Navier-Stokes equations with density-dependent viscosity and discontinuous initial data

In this paper, we consider the exterior problem for spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data. We prove that there exists a unique global piecewise regular solution for piecewise regular initial density with bounded jump discontinuity. In particular, the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially as .