Abstract
For degree-one equivariant maps on bounded domains, the question of finite-time blow-up vs. global existence of solutions to the harmonic map heat flow has been well studied. In this paper we study the Cauchy problem for degree- m equivariant harmonic map heat flow from ( 2 + 1 ) -dimensional space–time into the 2-sphere with initial energy close to the energy of harmonic maps. It is proved that solutions are globally smooth for m ⩾ 4 , whereas for m = 1 , we show that finite-time singularities can form for this class of data.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
