Archive for Rational Mechanics and Analysis

, Volume 161, Issue 2, pp 93-112

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

  • Michiel Bertsch Affiliated withDepartment 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
  • , Roberta Dal PassoAffiliated withDepartment 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
  • , Rein van der HoutAffiliated withAkzo Nobel Chemicals Research¶Arnhem, The Netherlands¶and Mathematical Institute¶University of Leiden¶Leiden, The Netherlands¶e-mail: rein.vanderhout@akzonobel.com

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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.