DG-MP-PDE Seminar: Ian Zwiers (UBC)

Vortex solitons are standing wave solutions with complex phase that is an (integer) multiple of the angular polar coordinate. This multiple we call the 'spin', and indexes a family of solutions with increasing L2 norm. In the case of no spin, Merle and Raphael have shown that there exists a range of data that blowup with the Townes profile (the regular soliton) and whose H1 norm grows at a precise 'log-log' rate. We prove that in the case of spin 1, there is comparable data that blows up with the vortex profile and the log-log rate. The case of spin 2 and 3 will be discussed. This is joint work with Gideon Simpson (Toronto)