隨著先進科技如航太科技,水下技術發展進步,微機電系統以及生物科技等發展，流體力學之應用與逐漸成為重要的研究目標之一，特別是針對流體之運動行為分析研究，進而期望達到預測及控制之目的。然而， Navier-Stokes 方程式為最能真實描述流體之運動行為的方程式，而此方程式由於相當複雜導致遲遲無人求得其解析解。
本文以一新穎的方法(偏微分方程之適應模糊解)求解二維 Navier-Stokes 方程式。目的是希望對二維 Navier-Stokes方程式與其幾何分析後之邊界條件求得一精確解。藉由模糊邏輯設計一粗略之模糊解，經數學推導以適應理論調整參數，其原理是以最佳化之方法將其誤差函數極小化而得。
本文首先以此適應模糊解求得一維Navier-Stokes 方程式模糊解，並將此模糊解與解析解比較得此差異極小，以驗證此方法之準確性。再以相同方法用於解二維 Navier-Stokes 方程式，可確保此二維 Navier-Stokes 模糊解為準確、完善。

With the development of technological, such as aeronautical engineering, ocean, naval mechatronics engineering, and MEMS, biomedical technology, the application of fluid dynamics becomes an important research objective, especially in the analysis of the motion behavior and are expected to achieve that forecast and control purposes. To describe the motion behavior of fluid, the Navier-Stokes Equation is generally adopted. However, the equation is quite complicated and there is still no analytical solution.
This study develops a new method, called adaptive fuzzy algorithm, for finding the solution of two-dimensional Navier-Stokes equations. The design objective is to find one fuzzy solution by the analysis of two-dimensional Navier-Stokes equations and the boundary conditions. The method is based on the fuzzy logical system to set up a rough fuzzy solution in the first and an adaptive law and optimum method are then investigated to minimize the error energy function for tuning the adjustable parameters of the proposed fuzzy solution.
First, this study uses the method to find the fuzzy solution of one-dimensional Navirer-Stokes equations, and compare the solution to exact solution to prove the accuracy of the method. Then, we can prove the method for solving the two-dimensional Navirer-Stoles Equation is robust and perfect.

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