On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications

By Laurent Desvillettes, Cédric Villani. 2000

175 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c48609ae754ea5cfe6a74ffa6b44756a9f52d0e1

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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, result): “Both approaches were unied and improved in more recent developments by Toscani and both authors [ 20 , 52], culminating with the second author’s close-tooptimal results [60] which were used in the present paper.”
Bismut formula for Lions derivative of distribution dependent SDEs and applications (2018, background): “On the other hand, because of crucial applications in the study of nonlinear PDEs and environment dependent financial systems, the distribution dependent SDEs (also called McKean-Vlasov or mean filed SDEs) have received increasing attentions, see [10, 11, 13, 14, 18, 22, 23] and references therein.”
Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential (2014, background): “MR 0470442 Zbl 0383.35064 [Desvillettes and Villani 2000a] L. Desvillettes and C. Villani, “On the spatially homogeneous Landau equation for hard potentials, I: Existence, uniqueness and smoothness”, Comm. Partial Differential Equations 25:1-2 (2000), 179–259.”
Distribution-Dependent SDEs for Landau Type Equations (2016, methodology): “e homogeneous Landau equation. These results provide pointwise estimates on the distributions, which are essentially diﬀerent from existing results on Lp-estimates and Sobolev regularities derived in [6, 7, 5] for the homogeneous Landau equation. 2 Existence, uniqueness and time-space continuity It ”
Almost Exponential Decay Near Maxwellian (2006, methodology): “This surprising new decay result relies crucially on recent energy estimates in Guo (2002, 2003a) as well as other extensive and delicate work (Desvillettes and Villani, 2000, 2001, 2002, 2005; Mouhot, 2005; Toscani and Villani, 1999; Villani, 2003).”
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds (2008, methodology): “The entropy method has lately been used in many situations: nonlinear diffusion equations (such as fast diffusions [DelPD, CV], equations of fourth order [CCT], Landau equation [ DV00 ], etc.), integral equations (such as the spatially homogeneous Boltzmann equation [TV1, TV2, V]), or kinetic equati”
ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS (2001, methodology): “further application in kinetic theory is to be found in the asymptotic analysis of the spatially homogeneous Boltzmann equation [ToVi99], and in its so called ‘grazing collisions limit’ given by the Landau-Fokker-Planck equation [DeVi97a], [ DeVi97b ].”
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates (2003, methodology): “Nearly all of the forthcoming discussion follows Otto and Villani [28].”
Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, methodology): “Known estimates for the Landau equation Lemma 30 (Lower bound - [22, 51]).”
Distribution dependent SDEs with singular coefficients (2018, unknown): “1 Introduction In order to characterize nonlinear Fokker-Planck equations using SDEs, distribution dependent SDEs have been intensively investigated, see [20, 15] and references within for McKean-Vlasov type SDEs, and [6, 7, 2] and references within for Landau type equations.”