初始旋度ω_0∈L（logL）~α（α＞1／2）的2－D　Euler方程弱解的存在性

Existence of Weak Solutions of 2-D Euler Equations with Initial Vorticityω_0 ∈ L (logL)￣α (α>1 /2 )

本文证明了当初始旋度ｗ０∈Ｌ（ｌｏｇＬ）α∩Ｌ１，α＞１／２时二维无粘Ｅｕｌｅｒ方程柯西问题整体解的存在性，其中Ｌ（ｌｏｇＬ）α（α＞１／２）是Ｚｇｇｍｕｎｄ函数类，在有界区域，它包含任意的Ｌｐ∩Ｌ１（Ｐ＞１）空间．另外，我们改正了文［２］中的一个猜测，即ｗ０∈Ｌ（ｌｏｇＬ）∩Ｌ１是整体解存在的临界情形．

In this paper we obtain the existence of global in time week .olutions of2-D invisid Eeler equations with initial vorticity w0 ∈ L (logL)α ∩ L1 which is theZygmund class and contains any space Lp ∩ L1 (P>1 ) in bounded domain . At thesame time we correct the remark of Mr Chae who claims that w0 ∈ L(logL) is thecritical case. The solutions is obtained by approximating the Euler equations byNavier-Stokes equations with the same initial data and then vanishing the viscosity.