Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian. (English) Zbl 07817669
Summary: The purpose of this paper is to show how the combination of the well-known results for convergence to equilibrium and conditional regularity, in addition to a short-time existence result, lead to a quick proof of the existence of global smooth solutions for the non cutoff Boltzmann equation when the initial data is close to equilibrium. We include a short-time existence result for polynomially-weighted \(L^\infty\) initial data. From this, we deduce that if the initial data is sufficiently close to a Maxwellian in this norm, then a smooth solution exists globally in time.
MSC:
| 35Q20 | Boltzmann equations |
Keywords:
Boltzmann equation; global existence; perturbation of equilibrium; conditional regularity; long-range interactionsReferences:
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