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Nonlinear Analysis

Dynamics of linearized 2d Navier Stokes equations in high Reynolds number regime(Joint Princeton-Rutgers Seminar on Analysis of Fluids)

Hao Jia, University of Minnesota

Location:  Hill 705
Date & time: Tuesday, 24 October 2023 at 1:40PM - 2:40PM

Abstract: Over the last decade there has been tremendous progresses in the study of fine dynamics of the linearized two dimensional Euler equations around shear flows or vortices, leading to a more or less complete understanding of important physical phenomena such as inviscid damping and vorticity depletion. For the corresponding Navier Stokes equations with a small viscosity, similar results are much harder to prove. On the technical level, this is a singular perturbation problem, and instead of Rayleigh equation (2nd order) one now needs to study, very precisely, the Orr-Sommerfeld equations (4th order) when the spectral parameter is close to the cluster of eigenvalues. 


 In this talk, we will review some recent advances in this direction and outline a unified approach to study uniform-in-viscosity inviscid damping, vorticity depletion and enhanced dissipation. Joint work with Rajendra Beekie (Duke) and Shan Chen (UMN). 

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