The Landau Equation in a Periodic Box

By Yan Guo. 2002

353 citations recorded by the source corpus.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/eb9948a4aaf9972d6b33386dc8fd8f68794ed7d2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Atomic and Molecular Physics, and Optics

Citations in the corpus

On the Landau approximation in plasma physics (2004, background): “It seems likely that the recent theorems proven by Guo [18, 19] are a plausible starting point for a complete treatment of the close-to-equilibrium setting.”
Smoothing Effects for Classical Solutions of the Full Landau Equation (2009, background): “The result of [18] can be summarized as follows Theorem 1.”
Short and long time behavior of the Fokker-Planck equation in a confining potential and applications (2005, methodology): “d, and [15] for the explicit exponential decay using hypoelliptic tools developed ﬁrst in [11], [9]. Recent results about more general kinetic equations on the Torus can be found in works by Guo (e.g [13]). We quote [7] for the convergence in t−N for all Nwith the use of entropy-dissipating methods,”
Hypocoercivity (2006, methodology): “- Finally, Yan Guo recently developed a new method [26], which he later pushed forward with Strain [46, 27], to get rates of convergence for nonlinear kinetic equations in a close-to-equilibrium regime.”
Factorization for non-symmetric operators and exponential H-theorem (2010, background): “l property also holds in L1 v H s x((1 + jvj)k 1=2), k>3=2. In [77, Theorems 1.1 & 3.1], quantitative spectral gap estimates are established in Hs v;x( 1=2), s2N, following partly ideas from [49, 50, 51, 97]. For the spatially homogeneous case, in [8] the decay estimate of etL was extended to”
The Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential (2010, methodology): “[20] Y. Guo, The Boltzmann equation in the whole space.”
Exponential Decay for Soft Potentials near Maxwellian (2008, background): “The estimate for the ∂iσ i term is exactly the same as in [9].”
Hypocoercive Diffusion Operators (2006, methodology): “By combining Theorem 3.7 with a linearization analysis and some global bounds derived by Yan Guo, Clément Mouhot and Lukas Neumann were able to recover a simple proof of the following theorem of convergence to equilibrium for the nonlinear Boltzmann equation.”
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation (2005, background): “Of course, these a priori bounds may be quite tricky; as a matter of fact, they have been established only in the spatially homogeneous situation (which means that the distribution function does not depend on the position variable; see the survey in [58]) or in a close-toequilibrium setting (see in ”
Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus (2006, methodology): “21) Now let us use some estimates proved in [18].”
Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, background): “Finally, we highlight the related results of regularisation for the Boltzmann equation without long-range interactions [19, 15, 16], and the related perturbative results for the Landau and (long-range interaction) Boltzmann equation [40, 38, 4, 5, 2, 62, 3].”
Enhanced dissipation and Hörmander's hypoellipticity (2021, methodology): “As a consequence, hypocoercive methods encounter two technical difficulties that are absent from our approach: 4See also the weighted energy method of Guo in [27].”
Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation (2009, background): “As for the existence of solutions, see [31] where unique weak solutions for spatially homogeneous case have been constructed with rather general initial data, and see [36] where the”
The Vlasov-Maxwell-Boltzmann system near Maxwellians (2003, methodology): “Let G1(v), G2 (v) be two number density functions for two types of particles with masses mi and diameters σi (i = 1, 2), then (p. 83 and p. 89 in [Ch]) Q(G1, G2)(v) is defined as”
Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators (2006, methodology): “The maximal domain is slightly bigger than this space, it is obtained in Guo (2002): h∈L2 M s.”
HYPOCOERCIVITY FOR LINEAR KINETIC EQUATIONS CONSERVING MASS (2010, neutral): “…[5,8,9,13]; based on hypoellipticity [20,22,23]; on hypocoercivity itself [21, 28, 35]; on applications of the so-called kinetic-ﬂuid decomposition [15–19 , Our purpose is to establish, in a simpliﬁed framework, suﬃcient conditions for proving hypocoercivity for a large class of linear kinetic…”
Classical Solutions to the Boltzmann Equation for Molecules with an Angular Cutoff (2003, methodology): “Although the method seems to work (in a simpler way) for hard potentials with γ 0 as well, the focus in this article is on the more interesting soft potentials with −3 12 ].”
Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential (2014, neutral): “Guo in [8] employs a completely different approach based on perturbation theory for the existence of periodic solutions to the spatially inhomogeneous Landau equation in R3.”
Hypocoercivity for kinetic equations with linear relaxation terms (2008, background): “The goal of this Note is to state hypocoercivity results in the two following cases:”