CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient.For regular initial data,we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically.When initial density is piecewise regular with jump discontinuity,we show that there exists a unique global piecewise regular solution.In particular,the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t → +∞.     

双极Navier-Stokes-Poisson方程整体解的存在性

考虑粘性系数依赖于密度的一维可压缩双极Navier-Stokes-Poisson(NSP)方程的初边值问题.首先对于一般初值证明了弱解的整体存在性,其次证明了真空状态若存在必在有限时间内消失.进一步,在真空消失之后,整体弱解变成强解并且以指数形式收敛到非真空平衡态.该文把文献[14]的结果推广到NSP的情形.