Abstract

We consider the half-wave equation with mass critical in two dimensions $$\{\begin{array}{c}i{u}_t=Du-\left|u\right|u,\hfill \\ u(t_0,x)=u_0(x),\hfill \end{array}$$ 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 $\Vert u_0{\Vert }_2=\Vert Q{\Vert }_2,$ where Q is the ground state solution of equation $DQ+Q=Q^2.$

中文翻译：

---

二维质量临界半波方程的非色散解

摘要

我们考虑二维质量临界的半波方程$$\{\begin{array}{c}\mathrm{一世}{你}_{吨}=D你-\left|你\right|你,\hfill \\ 你({吨}_0,X)={你}_0(X),\hfill \end{array}$$首先，我们证明了一族行孤波的存在。然后，我们展示了具有基态质量的有限时间爆破解的存在$\Vert {你}_0{\Vert }_2=\Vert 问{\Vert }_2,$其中Q是方程的基态解$D问+问={问}^2.$