Nondispersive solutions to the mass critical half-wave equation in two dimensions

作者：Georgiev, Vladimir^*; Li, Yuan

来源：Communications in Partial Differential Equations, 2022, 47(1): 39-88.

DOI：10.1080/03605302.2021.1950763

• Half-wave equation
• Traveling waves solution
• Ground state mass
• Finite-time blowup solution

We consider the half-wave equation with mass critical in two dimensions @@@ {iu(t)=Du-|u|u, @@@ u(t(0),x)=u(0)(x), @@@ First, we prove the existence of a family of traveling solitary waves. We then show the existence of finite-time blowup solutions with ground state mass ||u(0)||(2)=||Q||(2), where Q is the ground state solution of equation DQ+Q=Q(2).

• 单位
  5; 兰州大学; i