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Conservation of energy, weak transport and vanishing viscosity in 2D -- Lecture 3

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TUR - Mathematical aspects of turbulence: where do we stand?

The issue of inviscid energy dissipation is central in turbulence theory and much progress has been achieved recently through convex integration, with the construction of wild solutions. However, it remains unclear how physical are these wild solutions and, in particular, whether they can be obtained by vanishing viscosity limits. In planar inviscid flows a related problem is whether vorticity is indeed transported along irregular flows. In this lecture series we will explore conservation of energy and transport of vorticity along sequences of approximations to inviscid flows, especially small viscosity solutions of Navier-Stokes. We will focus on thresholds of regularity and mechanisms which avoid inviscid dissipation, both for energy and vorticity transport.

This talk is part of the Isaac Newton Institute Seminar Series series.

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