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Nonexistence of global solutions to the Cauchy problem for the damped nonlinear Schrödinger equations. (English) Zbl 0539.35022

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

MSC:

35J10 Schrödinger operator, Schrödinger equation
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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