Observations on the vanishing viscosity limit

Kelliher, James

doi:10.1090/tran/6700

Observations on the vanishing viscosity limit
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Trans. Amer. Math. Soc. 369 (2017), 2003-2027 Request permission

Abstract:

Whether, in the presence of a boundary, solutions of the Navier-Stokes equations converge to a solution to the Euler equations in the vanishing viscosity limit is unknown. In a seminal 1983 paper, Tosio Kato showed that the vanishing viscosity limit is equivalent to having sufficient control of the gradient of the Navier-Stokes velocity in a boundary layer of width proportional to the viscosity. In a 2008 paper, the present author showed that the vanishing viscosity limit is equivalent to the formation of a vortex sheet on the boundary. We present here several observations that follow from these two papers.

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