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Transition Threshold for the <scp>3D</scp> Couette Flow in Sobolev Space
- Source :
- Communications on Pure and Applied Mathematics. 74:2398-2479
- Publication Year :
- 2020
- Publisher :
- Wiley, 2020.
-
Abstract
- In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number $\text{Re}$. It was proved that if the initial velocity $v_0$ satisfies $\|v_0-(y,0,0)\|_{H^2}\le c_0\text{Re}^{-1}$, then the solution of the 3D Navier-Stokes equations is global in time and does not transition away from the Couette flow. This result confirms the transition threshold conjecture in physical literatures.
- Subjects :
- Conjecture
Applied Mathematics
General Mathematics
010102 general mathematics
Mathematics::Analysis of PDEs
Reynolds number
01 natural sciences
Physics::Fluid Dynamics
Sobolev space
010104 statistics & probability
symbols.namesake
symbols
0101 mathematics
Couette flow
Mathematics
Mathematical physics
Subjects
Details
- ISSN :
- 10970312 and 00103640
- Volume :
- 74
- Database :
- OpenAIRE
- Journal :
- Communications on Pure and Applied Mathematics
- Accession number :
- edsair.doi...........e716caedb090054978fbe2a627f6a57a