On the Boltzmann equation for long‐range interactions

By Radjesvarane Alexandre, Cédric Villani. 2002

214 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/11064496ba0140cf9e8abb445a937c107fe2d42a

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation (2005, background): “We recall that the study of the Cauchy problem for this equation, started by Carleman [10] in the thirties, is still far from completion, in spite of spectacular advances like the DiPerna-Lions theory [24] or its recent extension [1].”
On the Landau approximation in plasma physics (2004, methodology): “mathematical considerations on the Boltzmann and Landau equations; in particular we shall recall those results of [1] which will be useful here.”
Global Existence for Quadratic Systems of Reaction-Diffusion (2007, background): “[16, 1, 2] for Landau’s equation of plasma physics and Boltzmann’s equation without angular cutoff).”
Classical Solutions to the Boltzmann Equation for Molecules with an Angular Cutoff (2003, background): “In the presence of x dependence, very recently, global weak solutions have been constructed for the inverse power law without any angular cutoff, but up to some defect measures [ 2 ], see also [1].”
Global classical solutions of the Boltzmann equation without angular cut-off (2009, background): “When the physically relevant effects of these angular singularities are not cut-off, the only global spatially dependent theory we are aware of is the remarkable paper by Alexandre-Villani [5] from 2002, which proves the existence of DiPerna-Lions renormalized weak solutions [22] if one can add to t”
From Newton to Boltzmann: Hard Spheres and Short-range Potentials (2012, background): “Then the cross section actually becomes singular, so a different notion of limit must be considered, possibly in the spirit of Alexandre and Villani [3].”
The weak Harnack inequality for the Boltzmann equation without cut-off (2016, background): “As far as existence of weak solutions is concerned, Alexandre and Villani prove in [10] the existence of a certain type of renormalized solution.”
Cercignani's Conjecture is Sometimes True and Always Almost True (2003, background): “Theorem 6.1. Let 2 [0; 2 ]. Consider the following Kac-type master equation:”
Smoothing Effects for Classical Solutions of the Full Landau Equation (2009, unknown): “[23], [1] and [2]).”