The Boltzmann equation in the whole space

By Yan Guo. 2004

294 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/81bb13cecbff718c733a544ab7561b036f5e96e0

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In Applied Mathematics

In Atomic and Molecular Physics, and Optics

In Mathematical Physics

Citations in the corpus

Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff (2009, methodology): “Comparing to the cuto ff case, we aim to settle a mathematical framework similar to the studies first proved by Ukai, see [67, 68], and fitted into a energy method by Liu and collaborators [52, 53] and Guo [46] which has led to a clean th eory for the Cauchy problem in the cutoff case, for solutions”
A Kinetic Flocking Model with Diffusion (2010, methodology): “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 proofs are based on the analysis of so-called macroscopic equations; see [19, 20, 21, 22, 23] and [33, 35].”
Exponential Decay for Soft Potentials near Maxwellian (2008, methodology): “See [8, 11–13, 15, 16] for more applications of such a method.”
Decay of Dissipative Equations and Negative Sobolev Spaces (2011, background): “The existence of global solutions near Maxwellians has been established in various function spaces, see [31, 26, 28, 9, 20, 32, 10] for instance.”
Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus (2006, background): “For completeness we also refer to a recent preprint dealing with the problem in whole space [21] and the paper [26] for a related nonlinear energy method.”
The Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential (2010, methodology): “From [20], one has Pg = ( ag(t, x) + v.”
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”