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The relativistic Boltzmann equation near equilibrium. (English) Zbl 0814.35137

Yajima, K. (ed.), Spectral scattering theory and applications. Proceedings of a conference on spectral and scattering theory held at Tokyo Institute of Technology, Japan, June 30-July 3, 1992 in honour of Shige Toshi Kuroda on the occasion of his 60th birthday. Tokyo: Kinokuniya Company Ltd.. Adv. Stud. Pure Math. 23, 105-111 (1994).
Consider a gas with particle density \(F(x,t,v)\), where \(t = \text{time}\), \(x = \) position, \(v\) =momentum. Under some assumptions the inequality \[ \bigl | F (x,t,v) - \mu (v) \bigr | \leq c_ 1 e^{-\delta t} \sqrt {\mu(v)}, \quad 0 \leq t < \infty \tag{1} \] is true, where \(\mu (v) = e^{a + b \cdot v - c \sqrt {1 + | v |^ 2}}\) is the Maxwellian distribution. The inequality (1) means the asymptotic stability near equilibrium.
For the entire collection see [Zbl 0791.00025].

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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