Blowup of H1 solutions for a class of the focusing inhomogeneous nonlinear Schrodinger equation
Blowup of H1 solutions for a class of the focusing inhomogeneous nonlinear Schrodinger equation
In this paper, we consider a class of the focusing inhomogeneous nonlinear Schr\odinger equation \[ i\partial_t u + \Delta u + |x|^{-b} |u|^\alpha u = 0, \quad u(0)=u_0 \in H^1(\mathbb{R}^d), \] with $0<b<\min\{2,d\}$ and $\alpha_\star\leq \alpha <\alpha^\star$ where $\alpha_\star =\frac{4-2b}{d}$ and $\alpha^\star=\frac{4-2b}{d-2}$ if $d\geq 3$ and $\alpha^\star = \infty$ if …