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The Boltzmann equation with potential force in the whole space. (English) Zbl 1429.35169

Summary: We consider the Cauchy problem of the Boltzmann equation with potential force in the whole space. When some more natural assumptions compared with those of the previous works are made on the potential force, we can still obtain a unique global solution to the Boltzmann equation even for the hard potential cases by energy method, if the initial data are sufficiently close to the steady state. Moreover, the solution is uniformly stable.

MSC:

35Q20 Boltzmann equations
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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