Saved in:
Bibliographic Details
Main Author: Dutta, Anirban
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.00613
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917300858257408
author Dutta, Anirban
author_facet Dutta, Anirban
contents In this paper, we examine the averaging effect of a highly oscillating external force on the solutions of the Navier-Stokes equations. We show that, as long as the force time-average decays over time, if the frequency and amplitude of the oscillating force grow, then the corresponding solutions to Navier-Stokes equations converge (in a suitable topology) to the solution of the homogeneous equations with same initial data. Our approach involves reformulating the system as an abstract evolution equation in a Banach space, and then proving continuous dependence of solutions on both initial conditions and the external forcing.
format Preprint
id arxiv_https___arxiv_org_abs_2503_00613
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Note on Continuous dependence of Navier-Stokes equations with oscillating force
Dutta, Anirban
Analysis of PDEs
In this paper, we examine the averaging effect of a highly oscillating external force on the solutions of the Navier-Stokes equations. We show that, as long as the force time-average decays over time, if the frequency and amplitude of the oscillating force grow, then the corresponding solutions to Navier-Stokes equations converge (in a suitable topology) to the solution of the homogeneous equations with same initial data. Our approach involves reformulating the system as an abstract evolution equation in a Banach space, and then proving continuous dependence of solutions on both initial conditions and the external forcing.
title A Note on Continuous dependence of Navier-Stokes equations with oscillating force
topic Analysis of PDEs
url https://arxiv.org/abs/2503.00613