Global existence and blow-up for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential

Abstract

In this paper, we study the Cauchy problem for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential. We first establish the criteria for global existence and blow-up of general (not necessarily radial or finite variance) solutions to the equation. Using these criteria, we study the global existence and blow-up of solutions to the equation with general data lying below, at, and above the ground state threshold. Our results extend the global existence and blow-up results of Campos-Guzmán (Z.

L2 Concentration of Blow-Up Solutions for the Nonlinear Schrödinger Equation with an Inhomogeneous Combined Non-Linearity

“…For the well-posedness of (2), we refer the reader to [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the references therein. For the L 2 -critical case, a series of studies dealing with problem (2), we refer to [22][23][24][25][26][27] and the references therein.…”