Masashi Misawa, Nobumitsu Nakauchi. Source: Advances in Differential Equations, Volume 23, Number 9/10, 693--724.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.