Journal
ADVANCES IN MATHEMATICS
Volume 362, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2019.106963
Keywords
Euler and Navier Stokes equation; Inviscid damping; Enhanced dissipation; Kolmogorov flow; Metastability
Categories
Funding
- NSF of China [11425103]
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In this paper, we prove the linear inviscid damping and vorticity depletion phenomena for the linearized Euler equations around the Kolmogorov flow. These results confirm Bouchet and Morita's predictions based on numerical analysis. By using the wave operator method introduced by Li, Wei and Zhang, we solve Beck and Wayne's conjecture on the enhanced dissipation rate for the 2-D linearized Navier-Stokes equations around the bar state called Kolmogorov flow. The same dissipation rate is proved for the Navier-Stokes equations if the initial velocity is included in a bas in of attraction of the Kolmogorov flow with the size of nu(2/3+), here nu is the viscosity coefficient. (C) 2019 Elsevier Inc. All rights reserved.
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