Detail:

Abstract:

In 2006, Krieger, Schlag and Tataru constructed a family of type II blow up solutions to the 2+1 dimensional wave map equation with unit sphere as its target. A key feature of this family is that it exhibits a continuum of blow up rates. However, from its construction, the stability of this family was not clear. In this talk, I will present our recent work in which the stability of this family is proved within the equivariant framework. If time permits, we will also discuss some progress on the more general non-equivariant stability result. This is based on joint works with Joachim Krieger and Wilhelm Schlag.