Boundary Shape Control of the Navier-Stokes Equations and Applications |
| |
Authors: | Kaitai LI Jian SU and Aixiang HUANG |
| |
Institution: | 1.College of Science,Xian Jiaotong University,Xi’an,China |
| |
Abstract: | In this paper, the geometrical design for the blade’s surface \(\Im \) in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade’s surface and the existence of solutions of the equations for the Gäteaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary. |
| |
Keywords: | Blade Boundary shape control General minimal surface Navier-Stokes equations Euler-Lagrange equations |
本文献已被 CNKI 维普 万方数据 SpringerLink 等数据库收录! |
| 点击此处可从《数学年刊B辑(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学年刊B辑(英文版)》下载免费的PDF全文 |