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<p>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 external forcing.</p>

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A note on continuous dependence of Navier–Stokes equations with oscillating force

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Anirban Dutta

摘要

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 external forcing.