Singular solutions of the subcritical nonlinear Schrodinger equation

Abstract

We show that the subcritical $d$-dimensional nonlinear Schrödinger equation $i{\psi }_t+\Delta \psi +|\psi {|}^{2\sigma }\psi =0$, where $1<\sigma d<2$, admits smooth solutions that become singular in~$L^p$ for $p^{\ast }<p\le \infty$, where $p^{\ast }:=\frac{\sigma d}{\sigma d-1}$. Since ${\lim }_{\sigma d\to 2-}{p}^{\ast }=2$, these solutions can collapse at any $2<p\le \infty$, and in particular for $p=2\sigma +2$.

References in corpus (1)

• Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

Cited by in corpus (2)

• A sharp scattering condition for focusing mass-subcritical nonlinear Schrödinger equation
• Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schrödinger equation