Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
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Derives a boundedness-based continuation criterion for the Landau-Coulomb equation that rules out Type II approximately self-similar blow-ups slower than Type I without decay assumptions on the inner profile.
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Propagation of chaos for the Boltzmann equation with very soft potentials
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
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On Hydrodynamic Implosions and the Landau-Coulomb Equation
Derives a boundedness-based continuation criterion for the Landau-Coulomb equation that rules out Type II approximately self-similar blow-ups slower than Type I without decay assumptions on the inner profile.