On the spatially homogeneous landau equation for hard potentials part i : existence, uniqueness and smoothness

By Laurent Desvillettes, Cédric Villani. 2000

285 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/06a87374d0d81a8ce65f62f60f9639b2526a5a4b

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On the trend to global equilibrium in spatially inhomogeneous entropy‐dissipating systems: The linear Fokker‐Planck equation (2001, background): “), which can often be proven to hold independently of the problem of trend to equilibrium (see [15] for instance).”
Upper bounds for parabolic equations and the Landau equation (2015, background): “The following two lemmas are thus just an adaptation of the computation in [5] to the case of soft potentials.”
Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff (2009, background): “ncerning only the existence. An important step was initiated by the works of Desvillettes and his collaborators in 1990s, showing partial regularization results for some simpliﬁed kinetic models, cf. [26, 27, 28, 29, 33, 31, 72]. After the well knownresult ofDiPerna andLions[34] forthe cutoﬀcase, Li”
On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications (2000, methodology): “Note that as far as the evolution problem for the Landau equation with reasonable potentials is concerned, we need theorem 1 only for such smooth functions f , thanks to our study in [13].”
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 [7, 6], equations of fourth order [2], Landau equation [11], etc.”
On the Trend to Equilibrium for Some Dissipative Systems with Slowly Increasing a Priori Bounds (2000, methodology): “Taking into account possible vanishing of the kernel is easy but tedious [7, 11].”
Exponential decay toward equilibrium via entropy methods for reaction–diffusion equations (2006, methodology): “The entropy method has lately been used in many situations: nonlinear diffusion equations (such as fast diffusions [9,10], equations of fourth order [5], Landau equation [13], etc.”
Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential (2014, unknown): “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.”
Entropy Dissipation Methods for Degenerate ParabolicProblems and Generalized Sobolev Inequalities (2001, methodology): “In the linear case, one usually uses propagation of moments in order to study the smoothness of the solution, see for instance [25].”
Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation (2009, background): “review some related works on the regularizing eﬀect and the existence of solutions for the Landau equation. The regularizing eﬀect from the Landau collision operator has been rather well studied. See [31, 24, 13] for the spatially homogeneous case. For the spatially inhomogeneous problem, a regulari”
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 nancial systems, the distribution dependent SDEs (also called McKean-Vlasov or mean led SDEs) have received increasing attentions, see [10, 11, 13, 14, 18, 22, 23] and references therein.”