English

On uniqueness for the Harmonic Map Heat Flow in supercritical dimensions

Analysis of PDEs 2017-08-22 v5 Differential Geometry

Abstract

We examine the question of uniqueness for the equivariant reduction of the harmonic map heat flow in the energy supercritical dimension. It is shown that, generically, singular data can give rise to two distinct solutions which are both stable, and satisfy the local energy inequality. We also discuss how uniqueness can be retrieved.

Keywords

Cite

@article{arxiv.1601.06601,
  title  = {On uniqueness for the Harmonic Map Heat Flow in supercritical dimensions},
  author = {Pierre Germain and Tej-Eddine Ghoul and Hideyuki Miura},
  journal= {arXiv preprint arXiv:1601.06601},
  year   = {2017}
}

Comments

43 pages; typos corrected

R2 v1 2026-06-22T12:36:02.422Z