Tsutsumi, Masayoshi Nonexistence of global solutions to the Cauchy problem for the damped nonlinear Schrödinger equations. (English) Zbl 0539.35022 SIAM J. Math. Anal. 15, 357-366 (1984). The author studies the Cauchy problem for the equation \[ iu_ t=\Delta u+q(| u|^ 2)u-(ia/2)u,\quad x\in R^ n,\quad t>0,\quad u(x,0)=u_ 0(x),\quad x\in R^ n \] with \(a>0\) and a real function q. It is proved that the solution does not exist for all \(t>0\) under some assumptions about \(u_ 0,q\) (among others if \(u_ 0\) is of nonpositive energy). Reviewer: M.Kučera Cited in 2 ReviewsCited in 47 Documents MSC: 35J10 Schrödinger operator, Schrödinger equation 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:nonexistence; nonlinear Schrödinger equation; Cauchy problem PDFBibTeX XMLCite \textit{M. Tsutsumi}, SIAM J. Math. Anal. 15, 357--366 (1984; Zbl 0539.35022) Full Text: DOI