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

Abstract

We consider the half-wave equation $i{u}_t=Du-|u|u$ 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 $\Vert D^{\frac{1}{2}}u(t){\Vert }_{L^2}\sim \frac{1}{|t|}$ as $t\to 0^{-}$.

28 pages. arXiv admin note: substantial text overlap with arXiv:2007.15370

References in corpus (1)

• Numerical study of fractional Nonlinear Schrödinger equations