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

摘要/Abstract

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.

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

Abstract:

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.

Key words: Incompressible Euler equations, Axisymmetric Nozzles, Well-posedness, Convergence rates

中图分类号:

O175.2

林杰, 王天怡. 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[J]. 数学物理学报, 2023, 43(1): 219-237.

Lin Jie, Wang Tianyi. Well-Posedness and Convergence Rates of Three-Dimensional Incompressible Euler Flows in Axisymmetric Nozzles with Symmetric Body[J]. Acta mathematica scientia,Series A, 2023, 43(1): 219-237.

图/表 1

参考文献 34

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