Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat flow for harmonic maps between spheres

Author： Biernat Paweł   Bizoń Piotr  

Publisher： IOP Publishing

ISSN： 0951-7715

Source： Nonlinearity, Vol.24, Iss.8, 2011-08, pp. : 2211-2228

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Abstract

Using mixed analytical and numerical methods we investigate the development of singularities in the heat flow for corotational harmonic maps from the d-dimensional sphere to itself for 3 ≤ d ≤ 6. By gluing together shrinking and expanding asymptotically self-similar solutions we construct global weak solutions which are smooth everywhere except for a sequence of times &T_1Ti, and eventually the solution comes to rest at the zero energy constant map.

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