Introduction to the Potential Theory for the Time-Dependent Stokes System
暫譯: 時間依賴斯托克斯系統的潛能理論導論
Guenther, Ronald B., Roetman, Ernest
- 出版商: CRC
- 出版日期: 2026-07-13
- 售價: $7,110
- 貴賓價: 9.5 折 $6,754
- 語言: 英文
- 頁數: 164
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 0367408600
- ISBN-13: 9780367408602
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相關分類:
流體力學 Fluid-mechanics
尚未上市，無法訂購
相關主題
商品描述
Introduction to the Potential Theory for the Time-Dependent Stokes System is made up of two parts. The first part deals with a careful presentation of the principles on which the physical problems are based. The fluids under consideration are assumed to be incompressible and the equations so obtained are nonlinear. The linear problems are obtained by introducing characteristic parameters and so determining which terms can be neglected. The authors feel it is important that when a mathematical problem is solved, one knows precisely which problem has actually been solved. The second part deals with the mathematical treatment of the problems derived in the first part. These equations are linear and time dependent. The first step is the construction of a fundamental solution for the equations involved. They are analogous to the fundamental solutions for the potential and heat equations commonly found in the mathematical and engineering literature. The fundamental solution is used as in classical potential theory to construct solutions to initial and certain boundary value problems for the linear Stokes equations.
Features
- Careful presentation of the kinematics of fluid dynamics
- Derivation of the basic equations from first principles
- Rigorous treatment of the linearization of the equations leading to Reynolds and Euler numbers
- Derivation of the fundamental solutions for the Stokes and Oseen equations
- Explicit solutions to the Stokes and Oseen equations for initial value problems
- Potential theory for the Stokes system
- Comparison of compressible and incompressible fluids.
商品描述(中文翻譯)
《時間依賴的斯托克斯系統的勢理論介紹》由兩個部分組成。第一部分仔細介紹了物理問題所基於的原則。所考慮的流體假設為不可壓縮，所得到的方程式為非線性。通過引入特徵參數來獲得線性問題，從而確定哪些項可以被忽略。作者認為，在解決數學問題時，清楚地知道實際上解決了哪個問題是非常重要的。第二部分則處理第一部分中衍生的問題的數學處理。這些方程式是線性且時間依賴的。第一步是為所涉及的方程式構建基本解。它們類似於數學和工程文獻中常見的勢方程和熱方程的基本解。基本解用於像經典勢理論一樣，構建線性斯托克斯方程的初始和某些邊界值問題的解。
特點
- 流體動力學運動學的仔細介紹
- 從基本原則推導基本方程
- 對方程的線性化進行嚴謹處理，導出雷諾數和歐拉數
- 推導斯托克斯方程和奧辛方程的基本解
- 針對初始值問題的斯托克斯方程和奧辛方程的顯式解
- 斯托克斯系統的勢理論
- 可壓縮流體與不可壓縮流體的比較。
作者簡介
Ronald B. Guenther is an emeritus professor in the Department of Math-ematics at Oregon State University. His career began at the Marathon Oil Company where he served as an advanced research mathematician at its Den-ver Research Center. Most of his career was spent at Oregon State University, with visiting professorships at the Universities of Hamburg and Augsburg, and appointments at research laboratories in the United States and Canada, and at the Hahn-Meitner and Weierstrass Institutes in Berlin. His research inter-ests include mathematically modeling deterministic systems and the ordinary and partial differential equations that arise from these models.
Ernest Roetman (1936 - 2023) earned his Ph.D. in applied mathematics from Oregon State University in 1963. After a post doc at the University of Aachen, Germany, he took a position at Bell Labs. He began his academic ca-reer at Stevens Institute of Technology, New Jersey. Subsequently, he moved to the University of Missouri in Columbia, Missouri, with brief visiting positions at the University of Aachen, Germany, Oregon State University in Corvallis, Oregon, and the Marathon Oil Co. Research Center in Denver, Colorado. In 1980 he joined the Boeing Co. in Seattle, Washington as a researcher and manager. He retired from Boeing in 2003. He then taught mathematics and engineering courses at Henry Cogswell College, Everett, Washington until his final retirement in 2006.
作者簡介(中文翻譯)
羅納德·B·根瑟（Ronald B. Guenther）是俄勒岡州立大學數學系的名譽教授。他的職業生涯始於馬拉松石油公司，擔任其丹佛研究中心的高級研究數學家。他的大部分職業生涯都在俄勒岡州立大學度過，並曾在漢堡大學和奧格斯堡大學擔任訪問教授，還在美國和加拿大的研究實驗室以及柏林的哈恩-邁特納研究所和魏爾施特拉斯研究所任職。他的研究興趣包括數學建模確定性系統以及由這些模型產生的常微分方程和偏微分方程。
厄尼斯特·羅特曼（Ernest Roetman，1936 - 2023）於1963年在俄勒岡州立大學獲得應用數學博士學位。完成德國亞琛大學的博士後研究後，他在貝爾實驗室工作。他的學術生涯始於新澤西州的史蒂文斯科技學院。隨後，他轉到密蘇里州哥倫比亞的密蘇里大學，並在德國亞琛大學、俄勒岡州立大學（位於俄勒岡州科瓦利斯）和科羅拉多州丹佛的馬拉松石油公司研究中心擔任短期訪問職位。1980年，他加入位於華盛頓州西雅圖的波音公司，擔任研究員和經理。2003年他從波音退休。隨後，他在華盛頓州埃弗雷特的亨利·科格斯威爾學院教授數學和工程課程，直到2006年最終退休。
