相对论粘性流体的Müller-Israel-Stewart方程光滑解的破裂
Breakdown of smooth solutions to the Müller-Israel-Stewart equations of relativistic viscous fluids
AI总结：
该研究针对相对论粘性流体的Müller-Israel-Stewart方程，证明一类常状态局部化扰动的光滑初值对应的柯西问题解会有限时间破裂，还给出1+1维无黎曼不变量的结论及理想流体大数据奇点形成的更广义结果。
摘要：
我们研究四维Minkowski空间中描述具有体粘度的相对论粘性流体的Müller-Israel-Stewart型方程。我们证明存在一类光滑初值，它们是常状态的局部化扰动，对应的柯西问题唯一解会在有限时间内发生破裂。具体而言，我们证明这类解会在有限时间内形成奇点，或者在我们明确给出的意义下变得非物理。我们还证明，对于物理上相关的状态方程和粘度系数，1+1维下一般不存在黎曼不变量。最后，我们给出了Y. Guo和A.S. Tahvildar-Zadeh一项结果的更广义版本：我们在对状态方程非常一般的假设下，证明了理想流体的大数据奇点形成结果，允许流体声速取严格小于光速的任意值。
英文摘要：
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.
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