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

Abstract

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

16 pages

Cited by in corpus (1)

• Blow-up of non-radial solutions for the $L^2$ critical inhomogeneous NLS equation