Abstract
In this note we prove global in time existence of weak solutions of 2-0 Euler equations for incompressible fluid flows in the whole plane of R2 when the initial vorticity is in the Zygmund class L(log L). The solution is constructed by a vanishing viscosity limit of the sequence of solutions to the Navier-Stokes equations with the same initial data. This is a limiting case of the corresponding results of DiPerna and Majda in which global existence of weak solutions was obtained for initial vorticity in L1 ∩ Lp, 1 < p < ∞
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