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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2503.00613 |
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| _version_ | 1866917300858257408 |
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| 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 |