Mathematical Theory of a Fluid Flow Around a Rotating and Translating Body
暫譯: 旋轉與移動物體周圍流體流動的數學理論
Nečasová, Sárka, Kračmar, Stanislav, Neustupa, Jiří
- 出版商: Springer
- 出版日期: 2025-06-13
- 售價: $6,340
- 貴賓價: 9.5 折 $6,023
- 語言: 英文
- 頁數: 626
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031841190
- ISBN-13: 9783031841194
尚未上市，無法訂購
相關主題
商品描述
The book deals with qualitative analysis of the mathematical model of flow of a viscous incompressible fluid around a translating and rotating body. The considered mathematical model, which represents the description of the flow in a coordinate system attached to the body, is derived from the Navier-Stokes equations by means of an appropriate transformation. The core of the book is the mathematical theory of the transformed equations. Most of the text is devoted to the theory of the linearized versions of these equations (i.e. the Stokes- and Oseen-type equations), because they play a fundamental role in the theory of the complete nonlinear system.
Considering strong, weak, and very weak solutions, we present the L2 and Lq theories and the weighted space theory (with Muckenhaupt's weights) in the whole space and in an exterior domain. The book also contains the spectral analysis of the associated linear Stokes-Oseen-type operators and the information on semigroups generated by these operators, and related resolvent estimates.
Moreover, the book describes the asymptotic behavior of solutions and leading profiles of solutions for linear and as well as nonlinear systems.
Further, the book contains studies of the problem with artificial boundary (important in numerical analysis), an introduction to the theory of the corresponding complete nonlinear system in both steady and nonsteady cases, a brief description of the situation when the rotation is not parallel to the velocity at infinity and necessary estimates of the related Oseen kernels.
商品描述(中文翻譯)
本書探討了粘性不可壓縮流體在平移和旋轉物體周圍的數學模型的定性分析。所考慮的數學模型是從Navier-Stokes方程通過適當的變換推導而來，該模型描述了附著於物體的坐標系中的流動情況。本書的核心是變換方程的數學理論。大部分內容專注於這些方程的線性化版本的理論（即Stokes型和Oseen型方程），因為它們在完整非線性系統的理論中扮演著基本角色。
考慮強解、弱解和非常弱解，我們在整個空間和外部區域中呈現L2和Lq理論以及加權空間理論（使用Muckenhaupt的權重）。本書還包含了相關的線性Stokes-Oseen型算子的譜分析，以及這些算子生成的半群的信息和相關的解算估計。
此外，本書描述了解的漸近行為和線性及非線性系統解的主導輪廓。
進一步地，本書包含了帶有人工邊界的問題研究（在數值分析中很重要），對於相應完整非線性系統的理論的介紹，包括穩態和非穩態情況，簡要描述了當旋轉不與無窮遠處的速度平行時的情況，以及相關Oseen核的必要估計。
作者簡介
Sárka Nečasová was born in 1965. She studied mathematics at the Faculty of Mathematics and Physics (Charles University, Prague), graduated in 1988, and obtained her Ph.D. in 1991 (at the Czech Technical University in Prague). She defended her habilitation thesis at the University of Pau (France) in 2010, and she also achieved the Doctor of Sciences degree at the Czech Academy of Sciences in 2013. She worked as an assistant professor at the Czech Technical University in Prague in 1991-1995. In 1995, she became a researcher at the Mathematical Institute of the Academy of Sciences of the Czech Republic, Prague. She has been the head of the Department of Evolution Differential Equations since 2010. She obtained the following awards: the Wichterle prize (the prize of the Academy of Sciences of the Czech Republic for young researchers) in 2003; member of the Learned Society of the Czech Republic (since 2018, head of the section Mathematics and Physics 2020-2024, now the scientific secretary); and Praemium Academiae (awarded by the Czech Academy of Sciences) in 2021. She gave mini-courses at Zagreb (2017), Tata Institute Bangalore (2017), University of Wuerzburg (2018), and University of Nanjing (2020). Her main fields of interest are the mathematical analysis of models of fluids, partial differential equations, and qualitative theory.
Stanislav Kračmar was born in 1955. He obtained his master degree at Kharkov University, Kharkov, Ukraine, in 1980. Then he received the title RNDr. (MSc. equivalent) at the Faculty of Mathematics and Physics of the Charles University in Prague in 1982. He defended his Ph.D. thesis at the Czech Technical University in 1991 and his habilitation in 2001. He is currently Associate Professor at the Czech Technical University. His main fields of interest are mathematical modeling in mechanics of fluids, partial differential equations, and qualitative theory.
Jiří Neustupa was born in 1949. He defended his master degree in 1972 and his Ph.D. degree in 1977, both at the Charles University in Prague. He defended his habilitation in 1982. He became Full Professor in 1999. He worked at the Czech Technical University from 1977 to 2005. In 2005, he moved to the Mathematical Institute of the Czech Academy of Sciences. He gave mini-courses on the theory of the Navier-Stokes equations at the Petroleum Institute Abu Dhabi (2010, 2011), Banach Center Warsaw (2012), Waseda University Tokyo (2012), Tata Institute Bangalore (2014), and Yonsei University Seoul (2019). His main fields of interest are mathematical modeling in mechanics of fluids, partial differential equations, and qualitative theory.
Patrick Penel was born in 1948. He studied mathematics at the University of Paris-XI-Orsay, graduating in 1969. He defended his Ph.D. thesis in 1972 and his State Doctorate ès Science in 1975, both at Paris-XI-Orsay. He was appointed an assistant in Paris XIII (1969), he worked as an assistant professor in 1972-1974. He became Full Professor at the University of Toulon and Var in 1976 and stayed at this position until 2010. After having been appointed Emeritus Professor twice, he is now retired and honorary. His main fields of interest are mathematical fluid mechanics, partial differential equations, and their qualitative theory. He was a responsible manager for international university co-operations (Antananarivo-Madagascar 1980-1993, Prague-Czech Republic 1990-2017), and co-organizer of a series of international conferences in CIRM, Marseille-Luminy (2008, 2011, 2014, 2017). Furthermore, he has been Academician of Var since 2015, elected to Chair No. 15.
作者簡介(中文翻譯)
Sárka Nečasová於1965年出生。她在查爾斯大學（布拉格）的數學與物理學院學習數學，於1988年畢業，並於1991年獲得博士學位（在捷克科技大學）。她於2010年在法國保城大學辯護了她的晉升論文，並於2013年在捷克科學院獲得科學博士學位。她於1991年至1995年在捷克科技大學擔任助理教授。1995年，她成為捷克共和國科學院數學研究所的研究員。自2010年以來，她一直擔任演化微分方程系的主任。她獲得了以下獎項：2003年獲得維赫特萊獎（捷克共和國科學院頒發給年輕研究者的獎項）；自2018年以來成為捷克共和國學術學會成員（2020-2024年擔任數學與物理學部門主任，現為科學秘書）；以及2021年獲得捷克科學院頒發的Praemium Academiae。她在薩格勒布（2017年）、塔塔研究所班加羅爾（2017年）、維爾茲堡大學（2018年）和南京大學（2020年）舉辦了迷你課程。她的主要研究領域是流體模型的數學分析、偏微分方程和質量理論。
Stanislav Kračmar於1955年出生。他於1980年在烏克蘭哈爾科夫大學獲得碩士學位。然後，他於1982年在查爾斯大學的數學與物理學院獲得RNDr.（碩士學位等同）。他於1991年在捷克科技大學辯護了博士論文，並於2001年完成晉升。現在他是捷克科技大學的副教授。他的主要研究領域是流體力學中的數學建模、偏微分方程和質量理論。
Jiří Neustupa於1949年出生。他於1972年在查爾斯大學獲得碩士學位，並於1977年獲得博士學位。他於1982年完成晉升，並於1999年成為正教授。他於1977年至2005年在捷克科技大學工作。2005年，他轉至捷克科學院數學研究所。他在阿布達比石油研究所（2010年、2011年）、華沙巴拿赫中心（2012年）、東京早稻田大學（2012年）、班加羅爾塔塔研究所（2014年）和首爾延世大學（2019年）舉辦了有關Navier-Stokes方程理論的迷你課程。他的主要研究領域是流體力學中的數學建模、偏微分方程和質量理論。
Patrick Penel於1948年出生。他在巴黎第十一大學（Orsay）學習數學，於1969年畢業。他於1972年辯護了博士論文，並於1975年獲得科學國家博士學位，均在巴黎第十一大學完成。他於1969年在巴黎第十三大學被任命為助理，並於1972年至1974年擔任助理教授。他於1976年成為土倫與瓦爾大學的正教授，並一直擔任此職位至2010年。經過兩次被任命為名譽教授後，他現在已退休並擔任名譽職位。他的主要研究領域是數學流體力學、偏微分方程及其質量理論。他曾負責國際大學合作的管理（1980-1993年安塔那那利佛-馬達加斯加，1990-2017年布拉格-捷克共和國），並共同組織了一系列在馬賽-盧米尼CIRM舉辦的國際會議（2008年、2011年、2014年、2017年）。此外，自2015年以來，他一直是瓦爾的院士，當選為第15號主席。
