Large time behavior of the Vlasov-Navier-Stokes system on the torus

We study the large time behavior of Fujita-Kato type solutions to the Vlasov-Navier-Stokes system set on \(\mathbb{T}^3 \times \mathbb{R}^3\). Under the assumption that the initial so-called modulated energy is small enough, we prove that the distribution function converges to a Dirac mass in veloci...

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Bibliographic Details
Published in:arXiv.org 2019-12
Main Authors: Han-Kwan, Daniel, Moussa, Ayman, Moyano, Iván
Format: Article
Language:English
Subjects:
Distribution functions
Fine structure
Fluid dynamics
Fluid flow
Navier-Stokes equations
Toruses
Online Access:Get full text
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Summary:We study the large time behavior of Fujita-Kato type solutions to the Vlasov-Navier-Stokes system set on \(\mathbb{T}^3 \times \mathbb{R}^3\). Under the assumption that the initial so-called modulated energy is small enough, we prove that the distribution function converges to a Dirac mass in velocity, with exponential rate. The proof is based on the fine structure of the system and on a bootstrap analysis allowing to get global bounds on moments.
ISSN:2331-8422
DOI:10.48550/arxiv.1902.03864