Classical Solutions to the Boltzmann Equation for Molecules with an Angular Cutoff

By Yan Guo. 2003

201 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/85dd81e7f1f8c8fa72821f1a2e08300af8ebaf4a

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Boltzmann diffusive limit beyond the Navier‐Stokes approximation (2006, methodology): “We use the trick in [21] to split K as K = K 1−χ + K χ , where K 1−χ g ≡ ∫ μ(u)μ(v)|v −u| {1−χ (|u −v|)}g(u)B(θ)du dω − ∫ |v −u| μ(u){1−χ (|v −u|)}{μ1/2(u′)g(v′)+μ1/2(v′)g(u′)}du dω.”
Factorization for non-symmetric operators and exponential H-theorem (2010, methodology): “1], quantitative spectral gap estimates are established in Hs v,x(μ −1/2), s ∈ N∗, following partly ideas from [49, 50, 51, 97].”
The Vlasov-Maxwell-Boltzmann system near Maxwellians (2003, methodology): “The proof of (31) is based on direct estimates for those macroscopic equations (57) through (61) in the presence of {I − P} f, without using the averaging lemma as in [G1], [G2] and [ G3 ].”
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation (2005, background): “Here is a precise statement4: 4 At the moment, the constants in the following theorem are not explicit, since Guo’s estimates are partly based on compactness arguments.”
Exponential Decay for Soft Potentials near Maxwellian (2008, methodology): “As in [10], we will see in Lemma 2 that the singular part of K2, K 1−χ 2 , has stronger decay.”
Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators (2006, methodology): “In this work we shall extend and complete the works [10, 17, 21] and [7] by • giving a constructive proof of (1.”
Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus (2006, methodology): “In [20] the same method was also applied to the Boltzmann equation for cutoﬀ soft potentials.”