Existence of weak solutions of 2-D Euler equations with initial vorticity \(\omega_ 0\in L(\log^ +L)^ \alpha\) \((\alpha>0)\) (Q2565201)

The author proves the existence of a global weak solution to the two-dimensional incompressible Euler equations with initial vorticity belonging to the Orlicz space \(L(\log+L)^\alpha\) with \(\alpha>0\). This result improves an analogous result established recently by \textit{Y. Wu} [Ph. D. Thesis, Beijing, 1993] for \(\alpha>1/2\). The solution is obtained as a limit of the corresponding solutions of the Navier-Stokes equations as the viscosity tends to 0.