Julien Barré
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Léo Bigorgne
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Emanuele Caglioti
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Anwar El Rhirhayi
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Megan Griffin-Pickering
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Grace Mattingly
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Mario Pulvirenti
Is the BGK a toy model?
ABSTRACT: In this talk I consider the well known BGK equation, describing a rarefied gas close to the hydrodynamic regime. The starting point is the stochastic process associated to a particle system, which is known to be close to the mechanical behavior in a low-density regime. We (this is a work in collaboration with P. Butta’ and S. Simonella) plan to derive the BGK equation under a suitable scaling, giving a precise physical meaning to such an equation.
Stefano Rossi
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Frédéric Rousset
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Elena Salguero
Continuation Criteria for the Relativistic Vlasov–Maxwell System
ABSTRACT: The relativistic Vlasov–Maxwell (rVM) system is a fundamental model in kinetic theory describing the dynamics of collisionless plasmas with high-velocity particles. In the 1980s, Glassey and Strauss proved that solutions remain regular as long as the momentum support remains bounded in time, providing a key continuation criterion. Understanding the evolution of particle momentum is therefore central to establishing global existence of solutions. In this talk, we review known continuation criteria and present new insights in this direction. This is based on joint work with M. Hernandez and N. Patel.
Renato Velozo Ruiz
Phase mixing and the Vlasov equation in cosmology
ABSTRACT: In this talk, we will consider the Vlasov equation on expanding isotropic homogeneous tori described by the Friedmann–Lemaitre–Robertson–Walker cosmological spacetimes. For expansion rate $t^q$, with $0 < q \leq 1/2$ (excluding some exceptional values), we show that the difference of the spatial density with the spatial average decays with a quantitative rate depending on the regularity of the initial datum. This is joint work with Martin Taylor.