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arXiv · 2502.12733

Forced Rapidly Dissipative Navier--Stokes Flows

Lorenzo Brandolese·Takahiro Okabe
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Abstract

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.

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Lorenzo Brandolese, Takahiro Okabe. 2025-02-18. Forced Rapidly Dissipative Navier--Stokes Flows. https://doi.org/10.1137/22m1536807

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