具有宇宙学常数的Euler-Nordstrom系统的适定性
Well-Posedness for the Euler-Nordstrom System with Cosmological Constant
摘要：
本文考虑了在Nordstrom标量引力理论下具有自相互作用的相对论性理想流体的运动。流体的演化由一个拟线性双曲型偏微分方程组决定，并引入一个宇宙学常数以保证非零常数解的存在性。在此基础上，研究了无限延拓的静流体紧摄动的初值问题。虽然该系统既不是对称双曲也不是严格双曲，但Christodoulou关于从拉格朗日方程导出的方程的能量流存在的建设性结果可以适用于提供能量流，可以用来代替一阶对称双曲系统的标准能量原理。在给出这种能流后，作者利用它们证明了具有宇宙学常数的Euler-Nordstrom系统在适当的Sobolev空间中是适定的.
英文摘要：
In this paper the author considers the motion of a relativistic perfect fluid with self-interaction mediated by Nordstrom's scalar theory of gravity. The evolution of the fluid is determined by a quasilinear hyperbolic system of PDEs, and a cosmological constant is introduced in order to ensure the existence of non-zero constant solutions. Accordingly, the initial value problem for a compact perturbation of an infinitely extended quiet fluid is studied. Although the system is neither symmetric hyperbolic nor strictly hyperbolic, Christodoulou's constructive results on the existence of energy currents for equations derivable from a Lagrangian can be adapted to provide energy currents that can be used in place of the standard energy principle available for first-order symmetric hyperbolic systems. After providing such energy currents, the author uses them to prove that the Euler-Nordstrom system with a cosmological constant is well-posed in a suitable Sobolev space.
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