A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary
A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary
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DOI：
10.1080/03605302.2019.1583250
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发表时间：
2019-06-11
影响因子：
1.9
通讯作者：
Speck, Jared
中科院分区：
文献类型：
--
作者：
Hadzic, Mahir;Shkoller, Steve;Speck, Jared
研究了闵可夫斯基时空背景下的相对论欧拉方程。我们对状态方程和初始数据进行了假设，这些假设是众所周知的物理真空边界条件的相对论类比，这在非相对论性可压缩欧拉方程的先前工作中发挥了重要作用。我们的主要结果是推导，相对于拉格朗日（也称为共移）坐标，局部时间先验估计的解决方案。该解具有由流体四速度传递的流体-真空边界，沿该边界方程的双曲度退化。在这种情况下，相对论性欧拉方程等价于退化的拟线性双曲波图系统，不能用标准能量方法处理。
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.