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Blow-up for the damped \(L^2\)-critical nonlinear Schrödinger equation. (English) Zbl 1253.35022

Summary: We consider the Cauchy problem for the \(L^2\)-critical damped nonlinear Schrödinger equation. We prove existence and stability of finite time blow-up dynamics with the log-log blow-up speed for \(\|\nabla u(t)\|_{L^2}\).

MSC:

35B44 Blow-up in context of PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
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