带阻尼的非等熵欧拉方程组的爆破  

Blowup for the non-isentropic Euler equations with damping

作　　者：董建伟 杨永 DONG Jianwei;YANG Yong(School of Mathematics and Physics,Zhengzhou University of Aeronautics,Zhengzhou 450015,China)

机构地区：[1]郑州航空工业管理学院理学院,河南郑州450015

出　　处：《中山大学学报（自然科学版）》2018年第6期131-134,共4页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11501525);河南省杰出青年基金(2018JQ0004);河南省高等学校青年骨干教师资助计划项目(2013GGJS-142);郑州航空工业管理学院青年科研基金(2015113001)

摘　　要：研究带阻尼的非等熵欧拉方程组初边值问题解的爆破现象。利用积分方法证明了当与初始动量有关的加权泛函充分大时,其解将在有限时刻爆破。将近来已知的爆破结果由等熵情形推广到非等熵情形,并在没有绝热常数不大于3的限制下得到了负初始熵情形的爆破结果。The blowup phenomena of the solutions for the initial-boundary value problem of the non-isentropic Euler equations with damping is studied.It is proved that the solutions will blow up in finite time when a weighed functional associated with the initial momentum is large enough by using the integration method.Some recently known blow-up results are extended from the isentropic case to the non-isentropic case.And the blow-up result for the negative initial entropy case is obtained without the restriction that the adiabatic constant is not bigger than three.

关 键 词：带阻尼的非等熵欧拉方程组 初边值问题 爆破 

分 类 号：O175.2[理学—数学]