Energy critical Schrödinger equation with weighted exponential nonlinearity I: Local and global well-posedness

2017/10/17 by Bensouilah, Abdelwahab, Draouil, Dhouha, Majdoub, Mohamed
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.06477

Abstract

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with weighted exponential nonlinearity i∂_t u+Δu=(u)/(|x|^b)(e^α|u|2-1); (t,x) ∈ ℝ×ℝ², where 0< b <1 and α=2π(2-b). We establish local and global well-posedness in the subcritical and critical regimes.

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