中科院数学与系统科学研究院
数学研究所
调和分析及其应用中心
学术报告会
报告人：Dr. Miao Shuang(University of Michgan)
题 目：On the motion of the free boundary of a self-gravitating incompressible fluid
时 间：2016.08.04(星期四), 15:40--16:40
地 点：晨兴410室
摘要:
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.
