Transition threshold for the 2-D Couette flow in whole space via Green's function
| Autor: | Wang, Gaofeng, Wang, Weike |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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$$\|\omega_{0}\|_{H^{1}\cap L^1}\leq c_0\nu^{\frac{3}{4}}$$ for some small constant $c_0$ independent of the viscosity $\nu$, then we can reach the conclusion that the solution remains within $O\left( \nu ^{\frac{3}{4}}\right) $ of the Couette flow. Comment: 20pages |
| Databáze: | arXiv |
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