Blowup dynamics for inhomogeneous mass critical half-wave equation

Abstract

We consider the focusing inhomogeneous mass critical half-wave equation in one dimension. Under the mild conditions of the inhomogeneous factor, we show that the existence of the radial blowup solutions with ground state mass $\Vert u_0{\Vert }_2=\Vert Q{\Vert }_2$, where $Q$ is the unique positive ground state solution of equation $DQ+Q=Q^3$ and obtain the blowup rate $\Vert D^{\frac{1}{2}}u(t){\Vert }_{L^2}\sim \frac{1}{|t|}$ as $t\nearrow 0^{-}$.

arXiv comment32 pages