具耗散一维可压流体方程组奇性形成(英文)  

Formation of Singularities in One- dimensional Compressible Fluids with Dissipative Term

作　　者：刘法贵[1] 秦玉明[2] 

机构地区：[1]华北水利水电学院,郑州450008 [2]河南大学数学系,河南开封475001

出　　处：《郑州大学学报（理学版）》2002年第3期1-7,共7页Journal of Zhengzhou University:Natural Science Edition

基　　金：河南省创新人才基金资助项目;河南省骨干教师资助项目

摘　　要：考虑具耗散项 2 αu(α>0 )可压缩流体方程组 Cauchy问题经典解整体存在性与解的奇性形成 .如果熵和 α小于声波能量 ,证明了其经典解必在有限时间内产生激波 ,进一步给出了经典解的生命区间跨度估计 .The global existence and formation of singularities of classical solutions to the Cauchy problem in one dimensionalcompressible fluids with dissipative term 2au(α>0) are considered. It is proved that if the initial amount of the entropy and a are smaller than that of sound waves, then classical (periodic) solutions will develop shocks in a finite time. Moreover, some quantitative estimates of lifespan of classical (periodic) solutions and a result on global existence of classical solutions are given.

关 键 词：可压流体方程组 奇性 耗散 CAUCHY问题 经典解 整体存在性 生命区间跨度估计 

分 类 号：O354[理学—流体力学]