Boltzmann Equation: Micro-Macro Decompositions and Positivity of Shock Profiles

By Tai-Ping Liu, Shih-Hsien Yu. 2004

281 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/f0a32c82c07a59d0133a9345deecb3cafc2b7f14

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro–macro decomposition-based asymptotic-preserving method (2017, methodology): “(9) Themicro–macro decomposition, a useful tool for the study of the Boltzmann equation and its fluid dynamics limit [24], and for the design of asymptotic-preserving numerical schemes for kinetic equations [2,16,22], takes the form”
Stability of rarefaction waves of the Navier-Stokes-Poisson system (2014, background): “Among them, we only mention [13, 21, 22, 30, 31, 34, 36, 41] and reference therein.”
Mathematical tools for kinetic equations (2004, background): “Stationary Boltzmann equations are also important; see Arkeryd and Nouri [5] for weak solutions in a slab, Ukai and Asano [115] for strong solutions in an exterior domain with given Maxwellian at infinity and nearly compatible boundary conditions, or Liu and Yu [93] and the references therein for sh”
Numerical methods for kinetic equations* (2014, methodology): “foundations of the method were first proposed by Pareschi and Perthame (1996), inspired by previous works on the use of Fourier transform techniques (Bobylev 1988).”
The Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential (2010, methodology): “Recentl y, so utions inL(2)v framework were established by macro-micro decompositions and energy method for small perturbation of an equilibrium, cf [19, 20, 27, 28].”
The Green's function and large‐time behavior of solutions for the one‐dimensional Boltzmann equation (2004, background): “The characteristic information of the Euler equations is connected to operator P0ξ 1 on P0L2ξ [15]: dim(P0L 2 ξ ) = 3 , P0ξ 1Ei = λi Ei for i = 1, 2, 3, {λ1 = − √ 5/3, λ2 = 0, λ3 = √ 5/3 } , E1 ≡ (√ 3/2 χ0 − √ 5/2 χ1 + χ4 ) , E2 ≡ (−√2/3 χ0 + χ4), E3 ≡ (√ 3/2 χ0 + √ 5/2 χ1 + χ4 ) , (Ei , Ej ) = δij”