报告人：Qingtang Su(University of Michigan)
时间：2018-12-04 10:30-11:30
地点：Room 1303, Sciences Building No. 1
Abstract: In this paper, we study the motion of the two dimensional inviscid incompressible, infinite
depth water waves with point vortices in the fluid. We show that Taylor sign condition can fail if the
point vortices are sufficient close to the free boundary, so the water waves could be subject to the
Taylor instability. Assuming the Taylor sign condition, we prove that the water wave system is locally
wellposed in Sobolev spaces. Moreover, we show that if the water waves is symmetric with a certain
symmetric vortex pair traveling downward initially, then the free interface remains smooth for a long
time, and for initial data of size $\epsilon\ll 1$, the lifespan is at least $O(\epsilon^{-2})$.
