Entropy production for the Landau equation with Maxwell molecules is non-increasing after a finite time under moment and temperature-distribution conditions, partially resolving a 1966 conjecture.
Probabilistic Treatment of the Boltzmann Equation of Maxwellian Molecules
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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 the monotonicity of the entropy production in the Landau-Maxwell equation
Entropy production for the Landau equation with Maxwell molecules is non-increasing after a finite time under moment and temperature-distribution conditions, partially resolving a 1966 conjecture.
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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.