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[Lecture] Analysis and PDE Seminar——Long time behavior of 2d water waves with point vortices

DEC . 04 2018
Title: Analysis and PDE Seminar——Long time behavior of 2d water waves with point vortices 

Time: 10:30-11:30 am, Dec. 4, 2018, Tuesday

Venue: Room 1303, Sciences Building No. 1


Speaker: Qingtang Su (University of Michigan)


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 well-posed 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 $O(/epsilon^{-2})$.


Edited by: Guo Xinyu
Source: School of Mathematical Sciences