Kinetic equations and asympotic theory

By François Bouchut, François Golse, M. Pulvirenti, Benoit Perthame, Laurent Desvillettes. 2000

213 citations recorded by the source corpus.

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Citations in the corpus

On the Dynamics of Large Particle Systems in the Mean Field Limit (2013, methodology): “For more information on the Vlasov-Maxwell system, see [41, 17, 84].”
Chapter 1 – Gradient Flows of Probability Measures (2007, background): “The proof is based on a classical duality argument (see for instance [41, 7, 19]).”
DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV–POISSON PROBLEM (2012, methodology): “We refer to the surveys [30,10,26] for good account on the state of the art in the mathematical analysis and properties of the solutions of the Cauchy problem for the Vlasov-Poisson system.”
Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff (2009, result): “This is in sharp c ontrast to the cuto ff case, for which the theories have been well developed, see [19, 20, 21, 34, 36 , 6, 52, 53, 67, 68, 70] and the references therein.”
Existence, Uniqueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields (2009, background): “Good references are [64], Chapter 8 of [13], [30] and [61].”
Transport Equation and Cauchy Problem for Non-Smooth Vector Fields (2008, background): “Good references are [56], Chapter 8 of [12], [29] and [53].”
The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems (2011, background): “Good references are [64], Chapter 8 of [13], [30] and [61].”
A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources (2009, background): “The connection between kinetic and macroscopic fluid dynamics results from two properties of the collision operator [1,5]: (i) conservation properties and an entropy relation that imply that the equilibria are Maxwellian distributions for the zeroth order limit; (ii) the derivative ofQðf Þ satisfies”
A real space method for averaging lemmas (2004, unknown): “The one developed in [6] is quite simple but it still uses Fourier transform and Hardy spaces and it is only able to handle f 2 L p x;v with g 2 W ;p v L p x and the same exponent p.”
Hypoelliptic Regularity in Kinetic Equations (2003, background): “The classical averaging theory, developed in [11], [10], [9], [1], [14], [3], [15], [4], [5], state that the solution f(t; x; v) to a kinetic equation, say”
A review of the mean field limits for Vlasov equations (2014, background): “The proofs were partially completed in [98], [40], (see also [28] and [146]).”