Sharp bounds for the resolvent of linearized Navier Stokes equations in\n the half space around a shear profile

2017/03/02 by Emmanuel Grenier, Grenier, Emmanuel, Toan T. Nguyen +1
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.1703.00881

Abstract

In this paper, we derive sharp bounds on the semigroup of the linearized\nincompressible Navier-Stokes equations near a stationary shear layer in the\nhalf plane and in the half space (\ℝ₊² or \ℝ₊³), with\nDirichlet boundary conditions, assuming that this shear layer in spectrally\nunstable for Euler equations. In the inviscid limit, due to the prescribed\nno-slip boundary conditions, vorticity becomes unbounded near the boundary. The\nnovelty of this paper is to introduce boundary layer norms that capture the\nunbounded vorticity and to derive sharp estimates on this vorticity that are\nuniform in the inviscid limit.\n

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