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Global stability of Boltzmann equation with large external potential for a class of large oscillation data. (English) Zbl 1417.35091

Summary: In this paper, we investigate the stability of Boltzmann equation with large external potential in \(\mathbb{T}^3\). For a class of initial data with large oscillations in \(L_{x, v}^\infty\) around the local Maxwellian, we prove the existence of a global solution to the Boltzmann equation provided the initial perturbation is suitably small in \(L^2\)-norm. The large time behavior of the Boltzmann solution with exponential decay rate is also obtained. This seems to be the first result on the perturbation theory of large-amplitude non-constant equilibriums for large-amplitude initial data.

MSC:

35Q20 Boltzmann equations
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B45 A priori estimates in context of PDEs
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B20 Perturbations in context of PDEs
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