HELENA JUDITH NUSSENZVEIG LOPES, Universidade Federal do Rio de Janeiro
Authors: Peter Constantin, Milton C Lopes Filho, H. J. Nussenzveig Lopes and Vlad Vicol
2022 AWM Research Symposium
Analysis of Partial Differential Equations in Memory of David R. Adams

The inviscid limit problem for the incompressible Navier-Stokes equations in a bounded domain is a major outstanding open problem. Formally setting viscosity to zero yields the Euler equations but, in a bounded domain, the discrepancy in boundary conditions gives rise to boundary layer phenomena, something still poorly understood and which accounts for the difficulty in rigorously passing to the vanishing viscosity limit. In this talk I will discuss a criterion for a weak limit of vanishing viscosity to be a (weak) solution of the Euler equations. This criterion is given in terms of $\textit{vorticity concentration},$ instead of $\textit{energy concentration},$ which was extensively studied by R. DiPerna and A. Majda in the late 1980s. Time-permitting, I will discuss other instances where results for energy concentration contrast with those for vorticity concentration.

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