The Steady Navier-Stokes System: Basics of the Theory and the Leray Problem

這本書提供了數學流體力學中一個核心問題的成功解決方案：Leray問題，即在有界域中的定常Navier-Stokes系統的邊界值問題存在解的條件僅為總通量為零。這標誌著作者在過去幾年對Navier-Stokes方程研究中這個未被充分探索的主題上的工作的頂峰。這本書將是第一部詳細探討Leray問題的重要作品。結果以詳細的證明呈現，同時介紹了問題的歷史和先前的解決方法。此外，為了讀者的方便和文本的自給自足，還介紹了由穩態Stokes和Navier-Stokes系統描述的不可壓縮流體流動的數學理論基礎。對於這個活躍領域的研究人員來說，這本書將是一個寶貴的資源。

Mikhail Korobkov (born 17.09.1976) is an experienced researcher on the interaction of real analysis ("fine properties of functions") with nonlinear PDEs. He gained fame in mathematics after his joint papers with Jean Bourgain (Fields medal prize 1994, Princeton Institute for Advanced Study), and Jan Kristensen (University of Oxford), where they obtained the Morse--Sard type theorems for the sharp case of Sobolev mappings. M.Korobkov started his work at Novosibirsk State University and Sobolev Institute of Mathematics, had visiting positions in Italy and Lithuania, and now he has the full professor position at Fudan University, one of the oldest and most famous universities in China. M.Korobkov has more than 50 research papers, he participated in many international mathematical conferences with plenary talks, and he was also invited to present a series of plenary talks at school-conferences in various countries -- in Europe, in the USA, and in Japan.

Konstantin Pileckas got his Ph.D. from the Leningrad Branch of Steklov Mathematical Institute (LOMI) under the supervision of Prof. V.A.Solonnikov in 1982. In 1994 he received a habilitation from the University of Paderborn, Germany. From 1997 until 2008 he was head of the Department of Differential Equations at the Institute of Mathematics and Informatics in Vilnius. Since 2008 he is head of the Department of Differential Equations at Vilnius University. He is a member of the Editorial Board of several scientific Journals. K.Pileckas was twice awarded by Lithuanian National Science Prize. He is a member of the Lithuanian Academy of Sciences.

Remigio Russo has been full professor of Rational Mechanics from 1990 at the University ``Federico II'' of Naples and from 1993 to 2021 at the University of Campania ``L. Vanvitelli''. He was a visiting professor in several Universities (Kyoto, Bayreuth, Herriott-Watt of Edimburgh, Vilnius, etc.). His scientific interest has been essentially connected with well posedness problems (existence, uniqueness, continuous dependence upon data and stability) as well as qualitative properties of solutions to differential systems of mathematical physics, like the system of linear elasticity and viscous fluid (Stokes and Navier--Stokes systems). R. Russo has (co) authored over 60 original research papers. Since 1999 is a member of the Academy of Sciences of Naples.

米哈伊爾·科羅布科夫（Mikhail Korobkov）（出生於1976年9月17日）是一位研究實分析（'函數的細微性質'）與非線性偏微分方程交互作用的經驗豐富的研究員。在與讓·布爾甘（1994年菲爾茲獎得主，普林斯頓高等研究院）和揚·克里斯滕森（牛津大學）合作的論文中，他們獲得了關於Sobolev映射的銳利情況下的Morse-Sard型定理，從而在數學界聲名大噪。科羅布科夫在新西伯利亞國立大學和索博列夫數學研究所開始工作，曾在意大利和立陶宛擔任訪問學者，現在在中國最古老、最著名的大學之一復旦大學擔任正教授職位。科羅布科夫發表了50多篇研究論文，參加了許多國際數學會議並發表了主題演講，還應邀在歐洲、美國和日本等多個國家的學校會議上發表了一系列主題演講。

康斯坦丁·皮列茨卡斯（Konstantin Pileckas）於1982年在列寧格勒斯捷克洛夫數學研究所（LOMI）在瓦·A·索洛尼科夫教授的指導下獲得博士學位。1994年，他在德國帕德博恩大學獲得博士後資格。從1997年到2008年，他擔任維爾紐斯數學與信息學研究所的微分方程系主任。自2008年起，他擔任維爾紐斯大學微分方程系主任。他是多個科學期刊的編輯委員會成員。皮列茨卡斯兩次獲得立陶宛國家科學獎。他是立陶宛科學院的成員。

雷米吉奧·魯索（Remigio Russo）自1990年起擔任那不勒斯大學“費代里科二世”（Federico II）的有理力學教授，並自1993年起擔任坎帕尼亞大學“L. Vanvitelli”的教授，他曾在多所大學擔任訪問教授（京都、拜罗伊特、赫里奥特-瓦特的愛丁堡、維爾紐斯等）。他的科學興趣主要涉及良好設置問題（存在性、唯一性、對數據的連續依賴性和穩定性）以及數學物理微分系統的解的定性性質，如線性彈性系統和粘性流體（Stokes和Navier-Stokes系統）。魯索（合著）發表了60多篇原創研究論文。自1999年起，他是那不勒斯科學院的成員。