Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2404.11878 |
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Inhaltsangabe:
- In this paper, we investigate the transition threshold problem concerning the 2-D Navier-Stokes equations in the context of Couette flow $(y,0)$ at high Reynolds number $Re$ in whole space. By utilizing Green's function estimates for the linearized equations around Couette flow, we initially establish refined dissipation estimates for the linearized Navier-Stokes equations with a precise decay rate $(1+t)^{-1}.$ As an application, we prove that if the initial perturbation of vorticity satisfies$$\|ω_{0}\|_{H^{1}\cap L^1}\leq c_0ν^{\frac{3}{4}}$$ for some small constant $c_0$ independent of the viscosity $ν$, then we can reach the conclusion that the solution remains within $O\left( ν^{\frac{3}{4}}\right) $ of the Couette flow.