Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number

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On a new scale of borderline regularity spaces for Euler equations

Dr. Eitan Tadmor

CSCAMM, Dept. of Mathematics & IPST at University of Maryland

Abstract:   We introduce a new scale of spaces which measures borderline regularity in the incompressible Euler equations. This intermediate scale covers the gap between the weak Lorentz spaces and the larger Morrey spaces. It allows us to make wavelet-based subtle distinction in the N-dimensional borderline cases which separates between H^{-1}-compactness and the phenomena of concentration-cancelation. Expressed in terms of this new scale of spaces, borderline regularity in Euler equations is shown to be intimately related to uniform bounds of the coulomb energy and the vorticity configuration.

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