题目：Global well-posedness to the two-dimensional incompressible vorticity equation in the half plane

主讲人：酒全森

时间：11月12日 10:00-11:00

腾讯会议：610 873 360 

报告摘要：In this talk, we will present a self-contained proof of the global well -posedness in Sobolev spaces to the initial-boundary value problem of the two -dimensional incompressible vorticity equation in the half plane. That we prefer to use the vorticity instead of the velocity equation is partially due to the fact that the vorticity equation can be viewed as one of generalized surface quasi -geostrophic (SQG) equations, which attract more and more attentions and studies recently. The local well-posedness is proved via the contraction mapping principle. A contractive mapping is defined through solving the linearized equation and  an suitable  approximate system  is constructed and uniform estimates of the approximate solutions  are obtained to the linearized equation. Then  to show the global well-posedness, the expression of the gradient of the velocity and a Kato-type estimate of the gradient of the velocity through the vorticity will be presented.