Infinite time blow-up for half-harmonic map flow from $\mathbb{R}$ into ${\mathbb{S}}^1$

Yannick Sire, Juncheng Wei, Youquan Zheng

We study infinite time blow-up phenomenon for the half-harmonic map flow \begin{equation}\label{e:main00} \left\{\begin{array}{ll} u_t = -(-Δ)^{\frac{1}{2}}u + \left(\frac{1}{2π}\i…