A Note on Continuous dependence of Navier-Stokes equations with oscillating force
Analysis of PDEs
2026-03-03 v4
Abstract
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.
Keywords
Cite
@article{arxiv.2503.00613,
title = {A Note on Continuous dependence of Navier-Stokes equations with oscillating force},
author = {Anirban Dutta},
journal= {arXiv preprint arXiv:2503.00613},
year = {2026}
}