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SOME REMARKS ON THE NONLINEAR SCHRODINGER EQUATION WITH FRACTIONAL DISSIPATION.

Abstract : We consider the Cauchy problem for the L^ 2-critical focussing nonlinear Schrödinger equation with a fractional dissipation. According to the order of the fractional dissipation, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for$\| u(t) \|_L ^2$ .
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Mohamad Darwich, Luc Molinet. SOME REMARKS ON THE NONLINEAR SCHRODINGER EQUATION WITH FRACTIONAL DISSIPATION.. Journal of Mathematical Physics, American Institute of Physics (AIP), 2016, 57 (10), pp.101502. ⟨10.1063/1.4965225⟩. ⟨hal-01545104⟩

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