三维柱对称定常非齐次不可压Euler方程管道问题解的适定性及无穷远渐近速率  

Well-Posedness and Convergence Rates of Three-Dimensional Incompressible Euler Flows in Axisymmetric Nozzles with Symmetric Body

作　　者：林杰 王天怡 Jie Lin;Tianyi Wang(Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan 430070)

机构地区：[1]武汉理工大学理学院数学系,武汉430070

出　　处：《数学物理学报（A辑）》2023年第1期219-237,共19页Acta Mathematica Scientia

基　　金：国家自然科学基金(11971307)。

摘　　要：该文针对可以包含障碍物的三维柱对称无穷管道问题,运用流函数方法转化为椭圆方程的边值问题,利用能量估计和闸函数方法,证明了定常非齐次不可压Euler方程解的存在性和唯一性以及流线的非退化性即U>0.通过构造比较函数和极大值原理,在漩涡速度W不等于0的情况下,得到了两种边界的收敛速率:若无穷管道在有限长度以外是平边界,则方程的解以指数速率收敛到渐近状态;若无穷管道以多项式速率收敛到平边界,则方程的解以相同的多项式速率收敛到渐近状态.This paper studies the three-dimensional incompressible Euler flows in axisymmetric nozzles with a symmetric body.The well-posedness is established by stream function method and barrier function.Base on the above well-posedness,the far field convergence rates of the solutions are studied:if the infinite nozzles are the flat boundary outside the finite length,the solution of the equation converges to an asymptotic state at the exponential rate;if the infinite nozzles converge to the flat boundary with the polynomial rates,the solutions converge to the asymptotic states at the same polynomial rates.

关 键 词：非齐次不可压Euler方程 轴对称管道 适定性 渐近收敛速率 

分 类 号：O175.2[理学—数学]