Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published October 10, 2003 | Published
Journal Article Open

White Noise Limits for Inertial Particles in a Random Field

Abstract

In this paper we present a rigorous analysis of a scaling limit related to the motion of an inertial particle in a Gaussian random field. The mathematical model comprises Stokes's law for the particle motion and an infinite dimensional Ornstein-Uhlenbeck process for the fluid velocity field. The scaling limit studied leads to a white noise limit for the fluid velocity, which balances particle inertia and the friction term. Strong convergence methods are used to justify the limiting equations. The rigorously derived limiting equations are of physical interest for the concrete problem under investigation and facilitate the study of two-point motions in the white noise limit. Furthermore, the methodology developed may also prove useful in the study of various other asymptotic problems for stochastic differential equations in infinite dimensions.

Additional Information

© 2003 Society for Industrial and Applied Mathematics. Received by the editors January 14, 2003; accepted for publication (in revised form) May 21, 2003; published electronically October 10, 2003. This work was supported by the Engineering and Physical Sciences Research Council. The authors are grateful to R. Adler, D. Blömker, D. Elworthy, R. Kupferman, A.J. Majda, and J.C. Mattingly for useful suggestions. They are particularly grateful to N. O'Connell for providing them with the proof of Theorem A.1 and to P.R. Kramer for a very careful reading of an earlier version of the paper. They also thank the anonymous referee for many useful suggestions.

Attached Files

Published - s1540345903421076.pdf

Files

s1540345903421076.pdf
Files (244.1 kB)
Name Size Download all
md5:f1b911022f320d44ea9b051f44ab65d0
244.1 kB Preview Download

Additional details

Created:
September 15, 2023
Modified:
March 5, 2024