Seminar Event Detail

Differential Equations

Date:  Thursday, October 15, 2015
Location:  4088 East Hall (4:00 PM to 5:00 PM)

Title:  On the motion of the free boundary of a self-gravitating incompressible fluid

Abstract:   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 waves is replaced by the nonlinear self-gravity. In this talk, we 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 smooth data of size $\epsilon$, a unique solution exists and remains smooth for time greater than 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.


Speaker:  Shuang Miao
Institution:  Umich

Event Organizer:     


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