The free boundary problem of one-dimensional heat conducting compressible Navier–Stokes equations with large initial data is investigated. We obtain the global existence of strong solution under stress-free boundary condition along the free surface, where the heat conductivity depends on temperature $(\kappa = \overline{\kappa} \theta^b , b \in (0, \infty))$ and the viscosity coefficient depends on density $(\mu = \overline{\mu} (1 + \rho^a) , a \in [ 0, \infty))$. Moreover, the large-time behavior of the free boundary for the full compressible Navier–Stokes equations is also considered when the viscosity is constant and it is first shown that the interfaces which separate the gas from vacuum will expand outwards at an algebraic rate in time for all $\gamma \gt 1$.

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关于一维可压缩导热系数与温度相关的一维可压缩Navier-Stokes方程的自由边界问题

研究了一维具有较大初始数据的一维导热可压缩Navier-Stokes方程的自由边界问题。我们沿着自由表面在无应力边界条件下获得了强解的整体存在，其中导热系数取决于温度$（\ kappa = \ overline {\ kappa} \ theta ^ b，b \ in（0，\ infty ））$，粘度系数取决于密度$（\ mu = \ overline {\ mu}（1 + \ rho ^ a），\ in [0，\ infty））$。此外，当粘度恒定时，还考虑了完全可压缩的Navier-Stokes方程的自由边界的长时间行为，这首先表明，将气体与真空分离的界面将及时以代数速率向外扩展对于所有$ \ gamma \ gt 1 $。