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arXiv · 2503.00613

A Note on Continuous dependence of Navier-Stokes equations with oscillating force

Anirban Dutta
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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.

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Anirban Dutta. 2025-03-01. A Note on Continuous dependence of Navier-Stokes equations with oscillating force. https://doi.org/10.1007/s41808-025-00377-w

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