摘要
ＥＸＩＳＴＥＮＣＥＯＦＷＥＡＫＳＯＬＵＴＩＯＮＳＯＦ２－ＤＥＵＬＥＲＥＱＵＡＴＩＯＮＳＷＩＴＨＩＮＩＴＩＡＬＶＯＲＴＩＣＩＴＹω０∈Ｌ（ｌｏｇＬ~＋）~α（α＞１／２）￥ＷＵＹｏｎｇｈｕｉ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ａｃａｄｅ...
In this paper we obtain the existence of global in the weak solution of 2-D inviscid Euler equations with initial vorticity ω0 ∈L(log L)α ∩ L1 (α> i/2) which is of the Zygmund class and contains any space LP ∩ L1 (p>1). At the same time we correct the remark of Professor Chae who claims that ω0 ∈L(log L) is the critical case. Moreover, a counter-example shows that not all approximating solutions of the Euler equations whose vorticities contained in L(log L)α∩ L1 (α< 1/2) tend to a solution of the Euler equation,and in this sense our result is optimistical. The solution is obtained by approximating the Euler equations by Navier-Stokes equations with the same initial data and then making the viscosity vanish.
