外区域上可压缩Euler方程组的有限时间破裂  

Finite-time blow-up for the compressible Euler system in the exterior domain

作　　者：蔡律 赖宁安 周忆 Lv Cai;Ning'an Lai;Yi Zhou

机构地区：[1]复旦大学数学科学学院,上海200433 [2]浙江师范大学数学科学学院,金华321004

出　　处：《中国科学：数学》2024年第3期247-258,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12271487和12171097);复旦大学国际合作与交流处“双一流”(批准号:IDH6282016/032);浙江省自然科学基金(批准号:LY21A010009)资助项目。

摘　　要：本文研究高维(n=2,3)外区域中可压缩Euler方程组初边值问题解的长时间行为.假定初始密度和速度场在常状态附近有一个紧支集小扰动,本文证明带不可渗透边界条件的初边值问题没有整体解,并进一步给出解关于初值小扰动参数的生命跨度上界估计;引入一种比较简单的试探函数方法,并结合能量恒等式证明主要结论.In this paper,we consider the long-time behavior of the initial boundary value problem of the com-pressible Euler system in the exterior domain in high dimensions(n=2;3).Assuming the initial density and velocity admit small compactly supported perturbations near constant states,we show nite-time blow-up of the initial boundary value problem with the impermeable boundary condition.The upper bound of the lifespan estimate with respect to the small parameter of the initial perturbations is given.To this end,a test function method is introduced,which seems quite simple.The energy equality is also involved.

关 键 词：EULER方程组 可压缩 外区域 破裂 生命跨度估计 

分 类 号：O175[理学—数学]