On the motion of the free boundary of a self-gravitating incompressible fluid
主 题: On the motion of the free boundary of a self-gravitating incompressible fluid
报告人: Shuang Miao (University of Michigan)
时 间: 2016-08-07 9:30 - 10:30
地 点: Science building 1307
The motion of the free boundary of an incompressible fluid body subject to its self-gravitational force can be described by a free boundary problem of the Euler-Poisson system. This problem differs from the water wave problem in that the constant gravity in water wave is replaced by the nonlinear self-gravity. In this talk, we will present some recent results on the well-posedness of this problem and give a lower bound on the lifespan of smooth solutions. In particular, we show that the Taylor sign condition always holds; we prove that for small smooth data of size $\epsilon$, a unique smooth solution exists for time greater or equal to $O(1/\epsilon^{2})$. This is achieved by constructing an appropriate quantity and a coordinate change, so that the new quantity in the new coordinate system satisfies an equation without quadratic nonlinearity. This is a joint work with L.Bieri, S.Shahshahani and S.Wu.
