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Theme for TIFR Centre For Applicable Mathematics, Bangalore

Abstract:  Our knowledge of the regularity of solutions the 3D incompressible Navier-Stokes equations is incomplete, as described in my first lecture. A hierarchy of time averaged quantities first derived there will be shown to be connected to scaled higher moments of the vorticity field. These are a useful tool in analyzing how solutions behave. This is performed by looking at the behaviour of these scaled vorticity moments from 4 NS-data-sets. These show an unusual ordered behaviour which suggests and empirical relation between high $L^{p}$ norms and low norms. When this is inserted back into the analysis it indicates that the Navier-Stokes equations lie well within a region where solutions behave in a regular manner. This is joint work with D. Donzis, A. Gupta, R. M. Kerr, R. Pandit and D. Vincenzi.