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题目:Long time behavior of 2d water waves with point vortices




摘要:In this talk, 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 $-\frac{\partial P}{\partial\boldmath{n}}\geq 0$ can fail if point vortices are sufficient close to the free boundary, so the water waves could be subject to Taylor instability. Assuming 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 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 ate least $O(\epsilon^{-2}}$. The result can be extend to global and obtain modified scattering for localized initial data.


时间:2018年12月7日  8:40-10:00




邀请人:李军 老师