The Vlasov‐Poisson‐Boltzmann system near Maxwellians

By Yan Guo. 2002

328 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/fcdd36c40d56519147573b4e2d95c07457968349

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In Applied Mathematics

In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, methodology): “The compactness argument used in the proof is reminiscent of one used by Guo in [41] and of one used by the fourth author in [58].”
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”
Classical Solutions to the Boltzmann Equation for Molecules with an Angular Cutoff (2003, methodology): “Next, as in [ 11 ], with the smallness assumption of f, as well as the conservation laws (11), an analysis of the coefficients a, b and c through so-called macroscopic equations would imply � 1 0 ||Z(s)|| 2 ds CM.This is a contradiction to the normalization of Z(t, x, v), when M is small.”
Exponential Decay for Soft Potentials near Maxwellian (2008, methodology): “See [8, 11–13, 15, 16] for more applications of such a method.”
The Landau Equation in a Periodic Box (2002, methodology): “in [ G1 ], we demonstrate that although (11) is not true for general f( x, v), a similar type of estimates are indeed valid for any solution f (t, x, v) with small amplitude to (7):”
Stability of rarefaction waves of the Navier-Stokes-Poisson system (2014, unknown): “[3, 14, 15, 17].”
Decay of Dissipative Equations and Negative Sobolev Spaces (2011, methodology): “On the other hand, some analogous theorems of global existence and decay rate of the solutions to the Boltzmann equation with forces have also been established; see [34, 33, 6] for the Boltzmann equation with external forces, [7, 36, 35, 3] for the Vlasov-Poisson-Boltzmann system and [8, 30, 14, 4] ”
Decay and Continuity of the Boltzmann Equation in Bounded Domains (2008, background): “ds is uniformly bounded for the hard potentials, by (60) and (67), we deduce from the Averaging Lemma [DL], R χ(t,x)Zk(v)χv(v)dv are compact in L2([0,1] × Ω) for any smooth cutoﬀ function χ v(v) (see [G1]). It then follows that Z χZk(v)[1,v,|v|2] √ µdv are compact in L2([0,1]×Ω). Therefore, up to a ”
Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus (2006, methodology): “roof by a priori arguments, on a given smooth solution. The construction of positive solutions thanks to the estimates above is based on, by now standard, ﬁxed point arguments (we refer the reader to [18, 19] for instance). The function h = (f − f∞)f −1/2 ∞ satisﬁes Πg(h) = 0 and it solves ∂th = T(h”
A Kinetic Flocking Model with Diffusion (2010, background): “The following important observation, which plays a key role in the estimates on the macroscopic dissipation pointed firstly in [16] and later in [14], is that from (2.”
Boltzmann diffusive limit beyond the Navier‐Stokes approximation (2006, background): “The first version of such a positivity was in the integral sense [20]”