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 selfgravitating 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 EulerPoisson system. This problem differs from the water wave problem in that the constant gravity in water waves is replaced by the nonlinear selfgravity. In this talk, we present some recent results on the wellposedness 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.
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Speaker: Shuang Miao
Institution: Umich
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