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Nonuniqueness for the Heat Flow¶of Harmonic Maps on the Disk

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Abstract

We prove that for suitable initial data the heat flow of harmonic maps, from the disk to the sphere, admits infinitely many solutions, characterised by “backward bubbling” at some arbitrarily large time, all having uniformly bounded energy.

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Authors and Affiliations

  1. Department of Mathematics¶University of Tor Vergata¶Via della Ricerca Scientifica¶00133 Roma, Italy¶e-mail: bertsch@mat.uniroma2.it¶e-mail: dalpasso@mat.uniroma2.it, , , , , , IT

    Michiel Bertsch  & Roberta Dal Passo

  2. Akzo Nobel Chemicals Research¶Arnhem, The Netherlands¶and Mathematical Institute¶University of Leiden¶Leiden, The Netherlands¶e-mail: rein.vanderhout@akzonobel.com, , , , , , NL

    Rein van der Hout

Authors
  1. Michiel Bertsch
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  2. Roberta Dal Passo
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  3. Rein van der Hout
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Accepted June 26, 2001¶Published online October 30, 2001

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, M., Dal Passo, R. & van der Hout, R. Nonuniqueness for the Heat Flow¶of Harmonic Maps on the Disk. Arch. Rational Mech. Anal. 161, 93–112 (2002). https://doi.org/10.1007/s002050100171

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  • DOI: https://doi.org/10.1007/s002050100171

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