一维可压缩Navier-Stokes方程组整体弱解的存在性

Existence of the weak solution of the one dimensional compressible Navier-Stokes equations

研究了粘性依赖于密度的含外力项的一维可压缩Navier-Stokes方程组的自由边界问题。粘性系数μ(ρ)和压力P(ρ)为密度ρ的一般函数,并且外力项f为自变量x和t的函数。在适当的假设条件下,利用差分方法,得到了弱解的整体存在性和唯一性。为克服一般的粘性系数μ(ρ)和外力项f给研究带来的困难,文章得到了一些新的先验估计。

The free boundary for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity and extemal force is studied. Precisely, the viscosity coefficientμ（ρ） and the pressure P（ρ） are general functions of the densityρ , and the external forcefis function of independent variablexandt. Under certain assumptions, the global existence and uniqueness of the weak solution were obtained through the difference method. The present study obtains some new prior estimates for overcoming the difficulty in the similar research caused by the general viscosity coefficient μ（p） and the external forcef.