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Blow-up solutions to the nonlinear Schrödinger equation with oscillating nonlinearities. (English) Zbl 1162.35069

Summary: We investigate the possibility of finite time blow-up in \(H^1(\mathbb R^2)\) for solutions to critical and supercritical nonlinear Schrödinger equations with an oscillating nonlinearity. We prove that despite the oscillations some solutions blow up in finite time. Conversely, we observe that for a given initial data oscillations can extend the local existence time of the corresponding solution.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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