2+1维欧拉方程的奇异解（英文）  

Singular Solutions of the (2+1)-Dimensional Euler Equation

作　　者：刘希强[1] 刘睿[2] LIU Xi-qiang;LIU Rui(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China;School of Computer Science Liaocheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059 [2]聊城大学计算机学院,山东聊城252059

出　　处：《聊城大学学报（自然科学版）》2018年第1期1-5,28,共6页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金;中物院基金项目(11076015)资助

摘　　要：借助于推广的CK方法,获得了2+1维欧拉方程的等价变换和新旧解之间的关系。基于拉普拉斯方程的解,给出了构造欧拉方程某些显式解的公式,并列出了部分奇异解.利用所求出的等价变换及其求解公式,得到了2+1维欧拉方程一些随时间演化的新奇异解.By applying the generalized CK direct method,we obtain the equivalence transformations and the relationships of new and old solutions of the（2＋1）-dimensional Euler equation.Based on the solutions of Laplace equation,we get the formula to construct some explicit solutions and list some singular solutions of the Euler equation.By applying the equivalence transformations combined with the formula,we get some singular solutions with time varying of the （2＋1）-dimensional Euler equation.

关 键 词：欧拉方程 奇异解 等价变换 贝克隆变换 

分 类 号：O175.2[理学—数学]