This article is available for purchase or by subscription. See below.
Abstract
|
We study the large-time behavior of small-data solutions to the Vlasov–Navier–Stokes system
on
. We prove
that the kinetic distribution function concentrates in velocity to a Dirac mass supported at
, while the fluid velocity
homogenizes to
,
both at a polynomial rate. The proof is based on two steps, following the general
strategy laid out in HKMM: (1) the energy of the system decays with polynomial
rate, assuming a uniform control of the kinetic density, and (2) a bootstrap argument
allows us to obtain such a control. This second step requires a fine understanding of
the structure of the so-called Brinkman force, which follows from a family of new
identities for the dissipation (and higher versions of it) associated to the
Vlasov–Navier–Stokes system.
|
PDF Access Denied
We have not been able to recognize your IP address
3.15.151.214
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
fluid-kinetic PDEs, large-time behavior
|
Mathematical Subject Classification
Primary: 35Q83, 76D05
|
Milestones
Received: 14 August 2020
Revised: 19 April 2021
Accepted: 19 July 2021
Published: 11 May 2022
|
|