讨论了Ｂａｎａｃｈ极限时，往往考虑ｌ＾∞的平移子空间Ｍ＝｛ａ１，ａ２－ａ１，．．．ａｎ－ａｎ－１，．．．）｜｛ａｎ｝∈ｌ＾∞｝，本文找出了ｌ＾∞的单位球面Ｓ（ｌ＾∞）上距Ｍ的距离为１的一切点。......

In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics ......