EXISTENCE　OF　WEAK　SOLUTIONS　OF　2－D　EULER　EQUATIONS　WITH　INITIAL　VORTICITY　ω0∈L（logL~＋）~α（α＞1／2）  

作　　者：WU Yonghui(Institute of Systems Science, Acadetnia Sinica, Beijing 100080, China) 

出　　处：《Systems Science and Mathematical Sciences》1995年第3期234-239,共6页

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.

关 键 词：EXISTENCE EULER EQUATIONS Zygmund class N-function. 

分 类 号：O175.4[理学—数学]