Forced Rapidly Dissipative Navier--Stokes Flows
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915158092152832 |
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| author | Brandolese, Lorenzo Okabe, Takahiro |
| author_facet | Brandolese, Lorenzo Okabe, Takahiro |
| contents | We show that, by acting on a finite number of parameters of a compactly supported control force, we can increase the energy dissipation rate of any small solution of the Navier--Stokes equations in $\mathbb{R}^n$ . The magnitude of the control force is bounded by a negative Sobolev norm of the initial velocity. Its support can be chosen to be contained in an arbitrarily small region, in time or in space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forced Rapidly Dissipative Navier--Stokes Flows Brandolese, Lorenzo Okabe, Takahiro Analysis of PDEs We show that, by acting on a finite number of parameters of a compactly supported control force, we can increase the energy dissipation rate of any small solution of the Navier--Stokes equations in $\mathbb{R}^n$ . The magnitude of the control force is bounded by a negative Sobolev norm of the initial velocity. Its support can be chosen to be contained in an arbitrarily small region, in time or in space. |
| title | Forced Rapidly Dissipative Navier--Stokes Flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.12733 |