二维有外力欧拉方程组周期边界问题涡量梯度的增长  

Growth of Vorticity Gradient of the Periodic Incompressible Euler Equations with External Force

作　　者：梅文燚 邓大文[1] MEI Wenyi;TANG Taiman(School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,Hunan,China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《咸阳师范学院学报》2019年第2期36-41,共6页Journal of Xianyang Normal University

摘　　要：考虑二维有外力的不可压Euler方程组的周期边值问题,证明了存在梯度有幂指数增长的全局光滑解。通过对速度场的更仔细的估计,证明了在有外力但外力本身不增长的情况下存在梯度有幂指数增长的全局光滑解。有外力不可压Euler方程与无粘性无热传导Boussinesq方程组有相似之处,当中的涡量方程都有外力项,研究有外力不可压Euler方程对研究无粘性无热传导Boussinesq方程组的解的方法有借鉴意义。The periodic incompressible Euler equations with external force is investigated.It is shown that there is a smooth solution with vorticity gradient growing exponentially.Through a more careful estimation of the velocity field,it is proved that there is a global smooth solution with a power exp on ential growth in the case of external force but the force itself not growing.Euler equations with external force is similar to the inviscid Boussinesq system without heat conduction in that in both systems,the vorticity equation has a force term.Investigating the Euler equations with external force may throw lights on how to investigate the inviscid Boussinesq system without heat conduction.

关 键 词：不可压Euler方程组 周期边界条件 涡量梯度增长 外力 

分 类 号：O175.29[理学—数学]