一维黏性系数依赖于密度的非等熵Navier-Stokes方程的自由边值问题

The problem of free boundary for non-isentropic Navier-Stokes equations with density-dependent viscosity in one-dimension

本文得到了一维黏性系数依赖于密度的非等熵Navier-Stokes方程自由边值问题的全局经典解的存在性,其中黏性系数依赖于密度μ(ρ)=ρ~α+1,这里ρ表示流体的密度,α∈(0,+∞)为常数.与其他文献不同之处在于,本文先通过选取适当的能量泛函获得密度函数的上下界估计,从而大大降低了对常数α的限制,随后通过一系列先验估计,得到解的正则性,并且获得经典解的存在性证明.

In this article,we obtain the existence of global classical solutions for non-isentropic compressible Navier-Stokes equations with density-dependent viscosity in one-dimension.Here,let the viscosity coefficient beμ（ρ） = ρ^α ＋ 1,wnere ρ denotes the density of fluids and α ∈（0,＋∞） is a constant.The key point is that the positive upper and lower bounds of the density ρ are obtained by using some appropriate energy functionals,so it reduces the restriction to α enough.Moreover,we get the regularity of solutions by using a series of priori estimates and obtain the existence of classical solutions.