Gaussian Lower Bounds for the Boltzmann Equation without Cutoff

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The Vlasov-Poisson-Boltzmann/Landau system with polynomial perturbation near Maxwellian

“…For the non-cutoff Boltzmann equation, [41][42][43][44][45]53] obtains global regularity and long time behavior in a very general assumption by just assuming a uniformly bound in t, x such that…”

Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian

“…(2) Conditional regularity. In a series of recent works [22,19,16,15,14,17,18], global regularity estimates and lower bounds are obtained conditional only to certain macroscopic bounds. (3) A short-time existence result.…”

Local well-posedness of the Boltzmann equation with polynomially decaying initial data

“…Our interest in establishing local well-posedness with initial data that is merely polynomially decaying is due to its relationship to the recent conditional regularity program initiated by Silvestre [36] and continued in collaboration with Imbert and Mouhot [28][29][30][31][32][33]. The goal of the program is to understand the regularity theory for the Boltzmann equation conditional to the mass, energy, and entropy densities M (t, x) = f (t, x, v)dv, E(t, x) = f (t, x, v)|v| 2 dv and H(t, x) = f (t, x, v) log f (t, x, v)dv, satisfying, uniformly in (t, x),…”