Global existence, blow-up and mass concentration for the inhomogeneous nonlinear Schrödinger equation with inverse-square potential
Hui Jian,
Min Gong,
Meixia Cai
Abstract:<abstract><p>In the current paper, the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation including inverse-square potential is considered. First, some criteria of global existence and finite-time blow-up in the mass-critical and mass-supercritical settings with $ 0 < c\leq c^{*} $ are obtained. Then, by utilizing the potential well method and the sharp Sobolev constant, the sharp condition of blow-up is derived in the energy-critical case with $ 0 < c < \frac{… Show more
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