Blowup dynamics for mass critical Half-wave equation in 2D

Abstract: We consider the half-wave equation $iu_t=Du-|u|u$ in two dimensions. For the initial data $u_0(x)\in H^{s}(\mathbb{R}^2)$, $s\in\left(\frac{3}{4},1\right)$, we obtain the non-radial ground state mass blow-up solutions with the blow-up speed $|D^{\frac{1}{2}}u(t)|_{L^2}\sim\frac{1}{|t|}$ as $t\to 0^-$.