Type II Singularity Formation in Harmonic Map Flow

Friday, February 19, 2016 - 15:30 to 16:30
704 Thackeray
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Juncheng Wei
Professor
University of British Columbia

Abstract or Additional Information

We consider the harmonic map flow from a bounded two-dimensional domain to S2: u:ΩS2, ut=Δu+|u|2u. Here we don't assume any symmetry on the domain. We construct Type II blow up solutions and prove that the blow rate (Tt)/log2(Tt) is universal and stable in general domains. We also construct multiple and reverse bubblings. As a consequence we can perform a new geometric surgery for continuation of solutions after bubbling. If time permits, other Type II blow up problems, such as Keller-Segel and critical exponent problems will be discussed as well. (Joint work with Manuel del Pino and Juan Davila.)

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HOST: Huiqiang Jiang

Research Area