Fluids and Analysis Seminar

It is well-known that a sufficiently rapidly expanding spacetime can stabilize the fluid for relativistic/Einstein-fluid systems. One may wonder whether the expansion of the fluid, instead of the background spacetime geometry, is also able to achieve a similar stabilizing effect. As an attempt to address this question, we consider the free boundary relativistic Euler equations in Minkowski background \mathbb{M}^{1+3} equipped with a physical vacuum boundary, which models the motion of relativistic gas. For the class of isentropic, barotropic, and polytropic gas, we construct an open class of initial data which launch future-global solutions. Such solutions are spherically symmetric, have smallinitial density, and the support of which expands asymptotically linearly in time. In particular, the asymptotic rate of expansion is allowed to be arbitrarily close to the speed of light. Therefore, our main result is far from a perturbation of existing results concerning the classical Euler counterparts. This is joint work with Marcelo Disconzi and Chenyun Luo.