From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight

Briant, Marc, Merino Aceituno, Sara and Mouhot, Clement (2019) From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight. Analysis and Applications, 17 (1). pp. 85-116. ISSN 0219-5305

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Abstract

We study the Boltzmann equation on the d-dimensional torus in a perturbative setting around a global equilibrium under the Navier-Stokes lineari- sation. We use a recent functional analysis breakthrough to prove that the linear part of the equation generates a C0-semigroup with exponential decay in Lebesgue and Sobolev spaces with polynomial weight, independently on the Knudsen number. Finally we show a Cauchy theory and an exponential decay for the perturbed Boltzmann equation, uniformly in the Knudsen number, in Sobolev spaces with polynomial weight. The polynomial weight is almost optimal and furthermore, this result only requires derivatives in the space variable and allows to connect to solutions to the incompressible Navier-Stokes equations in these spaces.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0276 Mathematical statistics
Depositing User: Sara Merino Aceituno
Date Deposited: 04 Jun 2018 09:42
Last Modified: 23 Aug 2019 01:00
URI: http://sro.sussex.ac.uk/id/eprint/76285

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