论文标题
在二维中的质量临界半波动方程的非分散解决方案
Nondispersive solutions to the mass critical half-wave equation in two dimensions
论文作者
论文摘要
We consider the half-wave equation with mass critical in two dimension \begin{eqnarray*} \begin{cases} iu_t=Du-|u|u,\,\,\, \\ u(0,x)=u_0(x), \end{cases} \end{eqnarray*} First, we prove the existence of a family of traveling solitary waves.然后，我们显示具有最小质量$ \ | u_0 \ | _2 = \ | q \ | _2 $的有限时间爆炸解决方案的存在，其中$ q $是等式$ dq+q = q^2 $的基础状态解决方案。
We consider the half-wave equation with mass critical in two dimension \begin{eqnarray*} \begin{cases} iu_t=Du-|u|u,\,\,\, \\ u(0,x)=u_0(x), \end{cases} \end{eqnarray*} First, we prove the existence of a family of traveling solitary waves. We then show the existence of finite-time blowup solutions with minimal mass $\|u_0\|_2=\|Q\|_2$, where $Q$ is the ground state solution of equation $DQ+Q=Q^2$.
