Global regularity for solutions of the Navier-Stokes equation sufficiently close to being eigenfunctions of the Laplacian
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Bibliographic record
Abstract
In this paper, we will prove a new, scale critical regularity criterion for solutions of the Navier--Stokes equation that are sufficiently close to being eigenfunctions of the Laplacian. This estimate improves previous regularity criteria requiring control on the $\dot{H}^\alpha$ norm of $u,$ with $2\leq \alpha<\frac{5}{2},$ to a regularity criterion requiring control on the $\dot{H}^\alpha$ norm multiplied by the deficit in the interpolation inequality for the embedding of $\dot{H}^{\alpha-2}\cap\dot{H}^{\alpha} \hookrightarrow \dot{H}^{\alpha-1}.$ This regularity criterion suggests, at least heuristically, the possibility of some relationship between potential blowup solutions of the Navier--Stokes equation and the Kolmogorov-Obhukov spectrum in the theory of turbulence.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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