Metastability for the dissipative quasi-geostrophic equation and the non-local enhancement

Abstract

In this paper, we study the metastability for the 2-D linearized dissipative quasi-geostrophic equation with small viscosity $\nu$ around the quasi steady state ${\theta }_{sin}=e^{-\nu t}\sin y$. We proved the linear enhanced dissipation and obtained the dissipation rate. Moreover, the new non-local enhancement phenomenon was discovered and discussed. Precisely we showed that the non-local term re-enhances the enhanced diffusion effect by the shear-diffusion mechanism.

References in corpus (5)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Transition threshold for the 3D Couette flow in a finite channel
• Stability threshold of the 2D Couette flow in Sobolev spaces
• Pseudospectral and spectral bounds for the Oseen vortices operator
• Enhanced dissipation, hypoellipticity for passive scalar equations with fractional dissipation

Cited by in corpus (3)

• A dynamical approach to the study of instability near Couette flow
• Orientation mixing in active suspensions
• Enhanced dissipation, hypoellipticity for passive scalar equations with fractional dissipation