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Tristan Leger : Global existence, scattering, and propagation of moments for inhomogeneous kinetic equations. (Oct 15, 2024 3:10 PM)

The field of derivation of kinetic equations has seen many impressive advances recently. Yet the well-posedness and dynamics of these equations remain poorly understood. In this talk I will address such questions, and present a method to prove global existence, scattering and propagation of moments for inhomogeneous kinetic equations. It uses dispersive estimates for free transport, combined with kinetic theory techniques to deal with the specific difficulties brought by the structure of the equation under consideration (e.g. its cross section, the degree of the nonlinearity). I will discuss its concrete implementation for the kinetic wave and Boltzmann equations. This is based on joint work with Ioakeim Ampatzoglou.

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