Abstract We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has played an important role in prior work on the non-relativistic compressible Euler equations. Our main result is the derivation, relative to Lagrangian (also known as co-moving) coordinates, of local-in-time a priori estimates for the solution. The solution features a fluid-vacuum boundary, transported by the fluid four-velocity, along which the hyperbolicity of the equations degenerates. In this context, the relativistic Euler equations are equivalent to a degenerate quasilinear hyperbolic wave-map-like system that cannot be treated using standard energy methods.

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具有移动真空边界的相对论欧拉方程解的先验估计

摘要 我们研究了闵可夫斯基时空背景下的相对论欧拉方程。我们假设状态方程和初始数据是众所周知的物理真空边界条件的相对论类比，这在非相对论可压缩欧拉方程的先前工作中发挥了重要作用。我们的主要结果是相对于拉格朗日（也称为协同移动）坐标的解的局部时间先验估计的推导。该解具有流体 - 真空边界，由流体四速度传输，方程的双曲性沿该边界退化。在这种情况下，相对论欧拉方程等效于不能使用标准能量方法处理的退化拟线性双曲波图类系统。