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Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. (English) Zbl 1062.35137
Summary: We consider finite time blow up solutions to the critical nonlinear Schrödinger equation \(iu_t =- \Delta u - | u|^{\frac4N}u\) for which \(\lim_{t\uparrow T < +\infty}|\nabla u(t)|_{L^2} = +\infty\). For a suitable class of initial data in the energy space \(H^1\), we prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of \(L^2\) mass at the blow up point, the second part corresponds to the regular part and has a strong \(L^2\) limit at blow up time.

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