Weak Solutions of 2-D Euler Equations with Initial Vorticity in L(Log L)

✍ Scribed by D.H. Chae

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 415 KB
• Volume: 103
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1993.1052

✦ Synopsis

In this note we prove global in time existence of weak solutions of 2-D Euler equations for incompressible fluid flows in the whole plane of (R^{2}) 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 (L^{1} \cap L^{7}, 1<p<\infty). C 1993 Academic Press. Inc.