Abstract
In our previous papers, we introduce symphonic maps ([9]) and show a Hölder continuity of symphonic maps from domains of $\mathbb{R}^4$ into the spheres ([6], [7]). In this paper, we consider the heat flow of symphonic maps with values into spheres and prove a global existence of a weak solution to the Cauchy-Dirichlet problem for any given initial and boundary data.
Citation
Masashi Misawa. Nobumitsu Nakauchi. "Global existence for the heat flow of symphonic maps into spheres." Adv. Differential Equations 23 (9/10) 693 - 724, September/October 2018. https://doi.org/10.57262/ade/1528855476