Blow-up solutions of the intercritical inhomogeneous NLS equation: the non-radial case

In this paper we consider the inhomogeneous nonlinear Schrödinger (INLS) equation $$\begin{aligned} i \partial _t u +\Delta +|x|^{-b} |u|^{2\sigma }u = 0, \,\,\, x \in {\mathbb {R}}^N \end{aligned}$$ with $$N\ge 3$$ . We focus on intercritical case, where scaling invariant Sobolev index $$s_c=\frac{N}{2}-\frac{2-b}{2\sigma }$$ satisfies $$0<s_c<1$$ a previous work, for radial initial data in $$\dot{H}^{s_c}\cap \dot{H}^1$$ , prove existence of blow-up solutions and also lower bound rate. Here extend these results to non-radial case. an upper rate concentration result general finite time $$H^1$$