Journal ArticleDOI
Global solutions of Boltzmann's equation and the entropy inequality
R.J. DiPerna,Pierre-Louis Lions +1 more
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This article is published in Archive for Rational Mechanics and Analysis.The article was published on 1991-03-01. It has received 108 citations till now. The article focuses on the topics: Boltzmann's entropy formula & Gibbs' inequality.read more
Citations
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Compactness in Boltzmann’s equation via Fourier integral operators and applications. III
Journal ArticleDOI
General relative entropy inequality: an illustration on growth models
TL;DR: In this paper, the authors introduce the notion of General Relative Entropy Inequality for several linear PDEs, and give several types of applications of the GRIIN: a priori estimates and existence of solution, long time asymptotic to a steady state, attraction to periodic solutions for periodic forcing.
Book
Transport Equations for Semiconductors
TL;DR: In this paper, the Schr#x00F6 dinger equation is replaced by a macroscopic semi-classical model, and the Wigner equation is used.
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Lp regularity of velocity averages
TL;DR: In this paper, the authors present general regularity results for velocity averages, i.e. averages in ν of functions f(x, v) for which (v.∇x f) has some given regularity.
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On the Boltzmann equation for long-range interactions
TL;DR: In this article, a renormalized formulation of the Boltzmann equation without Grad's angular cutoff assumption was proposed, which allows the cross section to be singular in both the angular and the relative velocity variables.
References
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Journal ArticleDOI
On the Cauchy problem for Boltzmann equations: global existence and weak stability
TL;DR: In this article, the authors studied the large-data Cauchy problem for Boltzmann equations with general collision kernels and proved that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in L' to a solution.
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Global existence in L 1 for the modified nonlinear Enskog equation in ℝ 3
TL;DR: In this paper, a weak compactness argument for the modified Enskog equation in ℝ3 was presented, which is based on the existence of a Liapunov functional.