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On the Motion of a Self-Gravitating Incompressible Fluid with Free Boundary

Banff International Research Station for Mathematical Innovation and Discovery

We consider the motion of the interface separating a vacuum from an inviscid, incompressible, and irrotational fluid subject to self-gravitational force and neglecting surface tension in two space dimensions. We show that for smooth data which are size $\epsilon$ perturbations of an equilibrium state, the solution exists and remains smooth for time of at least $O(\epsilon^{-2})$. This should be compared with the lifespan $O(\epsilon^{-1})$ provided by local well-posedness. The key to the proof is to find a nonlinear transformation of the unknown function and a coordinate change, such that the equation for the new unknown in the new coordinate system has no quadratic nonlinear terms. This is a joint work with Lydia Bieri, Shuang Miao and Sohrab Shahshahani.

Mathematics; Fluid mechanics; Partial differential equations; Fluid dynamics

video/mp4

Author affiliation: University of Michigan

2017-05-03

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61453

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/