Dynamical collapse for cylindrical symmetric dipolar BEC

Abstract: In this talk, we consider a Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate. We will show that solutions arising from initial data with energy below the energy of the Ground State, and that do not scatter, blow-up in finite time. The proof is based on localization properties for the fourth power of the Riesz transforms, that we prove by means of some decay estimates of the heat kernel associated to the parabolic biharmonic equation, and pointwise estimates for the square of the Riesz transforms.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

Virtual Maxwell Analysis Seminar

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