论文标题
相对论粘性流体的müller-israel-stewart方程的平滑解决方案分解
Breakdown of smooth solutions to the Müller-Israel-Stewart equations of relativistic viscous fluids
论文作者
论文摘要
我们考虑了Müller-Israel-Stewart类型的方程式，描述了相对论的粘性流体，其四维Minkowski空间中具有较大的粘度。我们表明，存在一类平滑的初始数据，这些数据是恒定状态的局部扰动，在有限的时间内，针对Cauchy问题的相应独特解决方案分解了。具体来说，我们证明，在有限的时间内，这种解决方案在确切的意义上会发展出奇异性或变得毫无意义。我们还表明，对于物理相关的状态和粘度系数方程，通常不存在Riemann不变性。最后，我们提出了Y. Guo和A.S.的结果的更一般版本。 Tahvildar-Zadeh：我们证明，在状态方程式上非常一般的假设下，完美流体的大数据奇异性形成结果，使流体速度的任何值严格少于光速。
We consider equations of Müller-Israel-Stewart type describing a relativistic viscous fluid with bulk viscosity in four-dimensional Minkowski space. We show that there exists a class of smooth initial data that are localized perturbations of constant states for which the corresponding unique solutions to the Cauchy problem break down in finite time. Specifically, we prove that in finite time such solutions develop a singularity or become unphysical in a sense that we make precise. We also show that in general Riemann invariants do not exist in 1+1 dimensions for physically relevant equations of state and viscosity coefficients. Finally, we present a more general version of a result by Y. Guo and A.S. Tahvildar-Zadeh: we prove large-data singularity formation results for perfect fluids under very general assumptions on the equation of state, allowing any value for the fluid sound speed strictly less than the speed of light.
