Free boundary value problem for the one-dimensional compressible navier-stokes equations with density-dependent viscosity and discontinuous initial data

We study the free boundary value problem for one-dimensional isentropic compressible navier-stokes equations with density-dependent viscosity coefficient and discontinuous initial data in this paper. for piecewise regular initial density,we show that there exists a unique global piecewise regular solution,the interface separating the flow and vacuum state propagates along particle path and expands outwards at an algebraic time-rate,the flow density is strictly positive from blow for any finite time and decays pointwise to zero at an algebraic time-rate,and the jump discontinuity of density also decays at an algebraic time-rate as the time tends to infinity. © 2013 ruxu lian and guojing zhang.