2021/09/23 by Wettstein, Jerome
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2109.11458
In this paper, we continue to study the fractional harmonic gradient flow on Sn-1 taking values in a general closed manifold N ⊂ ℝn, addressing global existence and uniqueness of solutions of energy class with sufficiently small energy, adding to the existing body of knowledge pertaining to the half-harmonic gradient flow and expanding upon our previous work in [34]. We extend the techniques by Struwe in [30] and Rivière in [22] to the non-local framework analogous to [34] to derive uniqueness, employ commutator estimates as in [8] for regularity and follow [30] for a general existence result.