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Boltzmann to Landau from the Gradient Flow Perspective

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FKTW03 - Frontiers in kinetic equations for plasmas and collective behaviour

I will present recent joint work with José A. Carrillo and Matias Delgadino wherein we revisit the classical grazing collision limit which relates the famous Boltzmann equation to the Landau equation. By viewing the Boltzmann equation as a gradient flow due to Erbar, we employ some of the Γ-convergence ideas by Sandier and Serfaty to obtain convergence towards gradient flow solutions of the Landau equation. This is done by verifying the lower semicontinuous convergence of the metric derivatives and the upper gradients, the latter of which coincides with the entropy-dissipation functionals to these equations.  

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