We consider the local well-posedness of the one-dimensional nonisentropic Euler equations with moving physical vacuum boundary condition. The physical vacuum singularity requires the sound speed to be scaled as the square root of the distance to the vacuum boundary. The main difficulty lies in the fact that the system of hyperbolic conservation laws becomes characteristic and degenerate at the vacuum boundary. Our proof is based on an approximation of the Euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term. Then we construct the solutions to this degenerate parabolic problem and establish the estimates that are uniform with respect to the artificial viscosity parameter. Solutions to the compressible Euler equations are obtained as the limit of the vanishing artificial viscosity. Different from the isentropic case \cite{Coutand4, Lei}, our momentum equation of conservation laws has an extra term $p_{S}S_x$ that leads to some extra terms in the energy function and causes more difficulties even for the case of $\gamma=2$. Moreover, we deal with this free boundary problem starting from the general cases of $2\leq\gamma<3$ and $1<\gamma<2 $ instead of only emphasizing the isentropic case of $\gamma=2$ in \cite{Coutand4, jang1, Lei}.

中文翻译：

---

具有物理真空的非等熵欧拉方程的适定性

我们考虑具有移动物理真空边界条件的一维非等熵欧拉方程的局部适定性。物理真空奇点要求将声速缩放为到真空边界距离的平方根。主要困难在于双曲线守恒定律系统在真空边界处变得特征化和退化。我们的证明是基于通过退化抛物线正则化对欧拉方程的近似，该退化抛物线正则化是从退化人工粘度项的特定选择中获得的。然后我们构建这个退化抛物线问题的解决方案，并建立关于人工粘度参数的均匀估计。可压缩欧拉方程的解作为消失的人工粘度的极限获得。与等熵情况 \cite{Coutand4, Lei} 不同，我们的守恒定律动量方程有一个额外的项 $p_{S}S_x$，这导致了能量函数中的一些额外项，即使对于 $ 的情况也会造成更多困难γ=2$。此外，我们从 $2\leq\gamma<3$ 和 $1<\gamma<2 $ 的一般情况开始处理这个自由边界问题，而不是在 \cite{Coutand4 $ 中只强调 $\gamma=2$ 的等熵情况, jang1, Lei}。