Blowup dynamics for the mass critical half-wave equation in 2D

Abstract

We consider the two-dimensional half-wave equation $i{u}_t=Du-\left|u\right|u$. For the initial data $u_0\left(x\right)\in H^s\left(R^2\right)$, $s\in (\frac{3}{4},1)$, we obtain the existence of non-radial ground state mass blow-up solutions with the blow-up rate ${\Vert D^{\frac{1}{2}}u\left(t\right)\Vert }_{L^2}\sim \frac{1}{\left|t\right|}$ as $t\to 0^{-}$. This work extends the recent study by Georgiev and Li (2022) [9], which focused on constructing radial ground state mass blow-up solutions.