Paolo Galdi on the Occasion of His 60Th Birthday

Advances in Mathematical Fluid Mechanics

Rolf Rannacher · Adelia´ Sequeira Editors

Advances in Mathematical Fluid Mechanics

Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday

123 Editors Rolf Rannacher Adelia´ Sequeira Institut fur¨ Angewandte Mathematik Department of Mathematics Universitat¨ Heidelberg Centre for Mathematics and its Applications Im Neuenheimer Feld 293/294 Instituto Superior Tecnico/UTL´ 69120 Heidelberg Av. Rovisco Pais, 1 Germany 1049-001 Lisboa [email protected] Portugal [email protected]

ISBN 978-3-642-04067-2 e-ISBN 978-3-642-04068-9 DOI 10.1007/978-3-642-04068-9 Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2010920233

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Springer is part of Springer Science+Business Media (www.springer.com) Dedicated to Giovanni Paolo Galdi, on the occasion of his sixtieth birthday Giovanni Paolo Galdi Foreword

The present volume celebrates the 60th birthday of Professor Giovanni Paolo Galdi and honors his remarkable contributions to research in the field of Mathematical Fluid Mechanics. The book contains a collection of 35 peer reviewed papers, with authors from 20 countries, reflecting the worldwide impact and great inspiration by his work over the years. These papers were selected from invited lectures and contributed talks presented at the International Conference on Mathematical Fluid Mechanics held in Estoril, Portugal, May 21Ð25, 2007 and organized on the occasion of Professor Galdi’s 60th birthday. We express our gratitude to all the authors and reviewers for their important contributions. Professor Galdi devotes his career to research on the mathematical analysis of the Navier-Stokes equations and non-Newtonian flow problems, with special emphasis on hydrodynamic stability and fluid-particle interactions, impressing the worldwide mathematical communities with his results. His numerous contributions have laid down significant milestones in these fields, with a great influence on interdisci- plinary research communities. He has advanced the careers of numerous young researchers through his generosity and encouragement, some directly through intel- lectual guidance and others indirectly by pairing them with well chosen senior collaborators. A brief review of Professor Galdi’s activities and some impressions by colleagues and friends are included here. This project could not have been successfully concluded without the generous support of some collaborators and several Portuguese institutions. Special thanks are due to Joao˜ Janela for the careful preparation of the final version of this book, and also to Thomas Wick for his precious help. The financial and technical support of Fundaçao˜ para a Cienciaˆ e a Tecnologia (FCT), Fundaçao˜ Calouste Gul- benkian, Fundaçao˜ Luso-Americana para o Desenvolvimento (FLAD) and of Centro de Matematica´ e Aplicaçoes˜ (CEMAT), Instituto Superior Tecnico´ , are gratefully acknowledged. Finally, a special thanks to Springer-Verlag for accepting to publish this work. On behalf of all collaborators and friends of Professor G.P. Galdi we wish him many more years of continued high energy, great enthusiasm and further impressive mathematical achievements.

Heidelberg, Germany Rolf Rannacher Lisboa, Portugal Adelia« Sequeira

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Short Biography

Giovanni P. Galdi was born in Naples, Italy, on January 3, 1947, where he received his University degree (Laurea) in Physics from the University of Naples in 1971. He is, currently, the William Kepler Whiteford Professor of Engineering and Professor of Mathematics at the University of Pittsburgh. He is also Adjunct Faculty at the Tata Institute of Fundamental Research in Mumbai, India. Before joining the faculty at the University of Pittsburgh in the Fall semester 1999, in the years 1980Ð1985 he was Professor at the Department of Mathematics of the University of Naples (Italy) and, from 1985 until 1998, he was Professor at the Institute of Engineering of the University of Ferrara (Italy). Professor Galdi founded and organized the School of Engineering of the Uni- versity of Ferrara in 1989, where he was the Dean from 1989 until 1995. He has been Visiting Professor in several academic institutions, including the University of Glasgow (Scotland), University of Minnesota (USA), University of Paderborn (Ger- many), University of Pretoria (South Africa), TIFR, Bangalore (India), Fudan Uni- versity, Shanghai (China), University of Waseda, Tokyo (Japan), Czech Academy of Science (Czech Republic), Steklov Institute of Mathematics, the St Petersburg Branch (Russia), University of Paris-Sud XI, Orsay (France), Instituto Superior Tecnico, Lisbon (Portugal), and University of Pisa (Italy). In the years 2003 and 2009 he was awarded the Mercator-Gastprofessuren from Deutschen Forschungsgemeinschaft (DFG). He is a member of the Editorial Board of several scientific Journals, including European Journal of Mechanics B/Fluids. He is also co-founder and Editor in Chief of the Journal of Mathematical Fluid Mechanics, and of the Series Advances in Mathematical Fluid Mechanics, published by Birkhauser-Verlag,¬ Basel, Boston. Professor Galdi has (co) authored over 130 original research papers and 6 books, and (co) edited 13 books, dedicated mostly to hydrodynamic and mag- netohydrodynamic stability, mathematical theory of the Navier-Stokes equations, non-Newtonian fluid mechanics and fluid-solid interactions. In particular, his two- volume book “An Introduction to the Mathematical Theory of the Navier-Stokes Equation”, first published with Springer-Verlag in 1994, is a classical milestone in the steady-state theory of the Navier-Stokes equations.

Paolo Galdi – The Man and the Mathematician

During the 1960s I worked hard on the Navier-Stokes equations, writing a number of papers. Then I sensed that the problems weren’t getting easier, on top of which competition was moving in, so I looked for other things to do. My instincts soon found expression in reality when G.P. Galdi appeared on the scene; he would have been a formidable competitor and I’m happy I didn’t have to face that challenge. He had a voracious appetite for knowledge, and I recall repeated requests for reprints of my papers. At that time, e-mail was not yet suitable for exchanging manuscripts, and reprints were generally sent as hard copies through postal services. He requested an early paper, which I dutifully sent him. Postal service between USA and Italy was rather slow, and apparently he lost patience, as shortly later he requested the same paper again. I assumed then that he wanted a later paper, and sent him that one. That seems to have arrived prior to the one he wanted, as I then got still another request from him. Again there was confusion, and I sent him still another paper. Ever since, he has been repeatedly accusing me (publicly) of sending him things he didn’t want. Never mind! It is clear that he read all the papers (also those written by others), absorbed their content, and then carried the theory further in new ways that have left a permanent imprint with his signature. A case close to my heart is his 1997 paper with Heywood and Shibata, in which the dissertation problem that I gave to John Heywood about 1965, on which Heywood at the time made deep initial progress, was ﬁnally solved. Beyond that is his impressive recasting of my own results on exterior problems into function space settings, and his extensions of the results to rotating and more general periodic motions. Galdi became Ð and continues to be Ð a central ﬁgure in describing and clarifying some of the most profound problems in modern hydromechanics. He has established himself as one of the few top contributors to a theory that has attracted worldwide interest and activity, and as a person who has stimulated and encouraged the creative achievements of many others. He is in fact in large part responsible for the present worldwide interest, by calling attention to the beauty, depth and underlying unity of the many open problems.

Stanford, California Robert Finn

xi xii Paolo Galdi Ð The Man and the Mathematician

As many people have commented, “Paolo Galdi is a very special person”. His enthusiasm, generosity, kindness and discernment have made him a most valu- able colleague to the whole community of researchers working on topics in fluid dynamics. Paolo’s own contributions to fluid dynamics have been very significant and wide ranging. As an Editor of the Handbook of Mathematical Fluid Dynamics,Iwasvery pleased to include an article by Paolo “On the motion of a rigid body in a viscous fluid” which covered an interesting sub-class of important fluid applications, and illustrated Paolo’s versatility. Through hard work and dedication, Paolo, John Heywood and Rolf Rannacher have created a major journal in the field, The Journal of Mathematical Fluid Dynam- ics, which has encouraged the resurgence of a classical topic in mathematics that is again taking center stage in partial differential equations. I was honored and delighted to be part of the wonderful celebration of Paolo’s 60th birthday that Adelia« Sequeira and her colleagues organized in Estoril in 2007.

Los Angeles, California Susan Friedlander

I am not sure when I first met Paolo. I think it was in 1976 when I published my book on the stability of fluid motions. The mathematicians in Naples, under Salvatore Rionero, had taken an interest in the energy theory of stability. Paolo was a student of Rionero. I had published papers on that subject which led to my 1976 book on the stability of fluid motions. I was greatly stimulated to go in this direction by papers of James Serrin. I think that Mariolina Padula, Paolo’s wife then, was also Rionero’s student. She was, in any case, very active in math and she and Paolo would study together. Paolo and Mariolina came to the US I think in 1976. I do not know how their trip was financed. In any case, my wife then (Ellen) and I had a little party in our house which was on a lake in Minnesota. James Serrin was also a guest. I think it was in 1976 because Paolo reminded me that my book had arrived from Springer that very day. I think that Paolo and Mariolina were very impressed to meet with persons they though so great in an environment so different that via Mezzacannone. This is the time that Paolo and I became fast friends. I like to say that people from Minneapolis and Naples are natural friends since Minneapolitans can be thought to be small persons from Naples. The next stage of our friendship developed in successive trips to Italy. These trips were arranged by Professor Rionero. In the first trip, Paolo and Mariolina invited me to their home. There, I learned about Paolo’s special talents in the arts as a painter specializing in portraits of Donald Duck and as a fine pianist specializing in Chopin. I loved Naples. For years in the early 1980s I taught in the summer school in Ravello. These were very pleasant summers. In 1982, I practiced there to run the original marathon in Greece. I would run up to Valico di Chiunzi and back, chased always by angry Italian dogs. The further south you go in Europe, the greater are the number of female math students and there were many nice ragazzi Paolo Galdi Ð The Man and the Mathematician xiii in Ravello. I remember one handsome Italian mathematician from Bologna telling me that his marriage license was not valid in the South. Later, it was not valid in the north. I had many intimate conversations with Paolo in the cafes in Ravello. At this time he was drifting to a more rigorous approach to mathematics. I urged him to continue his studies on the applied side, warning him that if he followed his desire he would have to compete with fine mathematicians much better prepared than he. At that time, he was working on energy theory on unbounded domains. To complete his results, he needed some powerful Navier Stokes theorems. I think the work of Leray was involved in his theorems. He was intense about mathematics and had gone beyond the energy theory of stability which frankly is a theory which demands that you know how to use the divergence theorem and integrate by parts. Gradually, our trajectories in science grew apart. Paolo was encouraged to prepare his now well known Springer monograph on the Navier Stokes equations by Clifford Truesdell, who at an earlier time was also my mentor but later my tormentor. In 1991, Paolo and Salvatore visited me again in Minneapolis. I had developed a theory for miscible liquids and showed that mixtures of incompressible mixing liquids are compressible and obtained a new theory of diffusion. The velocity is not solenoidal. Paolo found that a certain combination of the velocity and expansion velocity was divergence free. It turns out that this combination is equivalent to a volume averaged velocity. It is a great result, which we used in all subsequent papers. Paolo is a very special, outgoing and supportive person. He has that magic per- sonality which radiates interest and concern about others wherever he goes. He engages all persons and elevates their level of well being. Maybe this is why he has so many friends all over the world and at the great birthday meeting celebrated by this volume. I know three mathematicians from the applied side who developed a burning desire to be the master of rigorous mathematics. This goal is at the top of a mountain. One of these mathematicians in Klaus Kirchgassner,¬ another is Edward Fraenkel and the third is Paolo. It was a difficult journey, but Paolo has reached the summit without forgetting the applied side. It is my pleasure to wish happy 60th birthday to this good friend, great man and fine mathematician.

Minneapolis, Minnesota Daniel D. Joseph

Naples, via Mezzocannone, 8, early Seventies. It is here, in this stern and monu- mental environment where Tommaso d’Aquino gave his theological lectures, that I, a young student of Mathematics, take my first steps in the field of mathematical research. Professor Salvatore Rionero introduces and guides me into this world where at first I feel awe. Further than him, I owe his young co-worker Giovanni Paolo Galdi my quick and complete adaption, so that I could feel quite at ease xiv Paolo Galdi Ð The Man and the Mathematician among those great staircases and those lecture halls where one could smell the odor of history. There had lived and worked mathematicians of the level of Ernesto Cesaro, Roberto Marcolongo, Mauro Picone and Renato Caccioppoli and there still worked in that period great masters like Alfredo Franchetta, Carlo Miranda and Carlo Tolotti. Paolo, as I called him at once since at once we became friends, was for me a most precious guide towards that world which seemed to me very far and difficult to reach. Paolo addressed me to the journals he deemed more suitable for my kind of research, gave me his advice, but above all stimulated me with his observations and his sparkling conversation. Our friendship and our work relations consolidated in time. I always remember the wonderful evenings passed together, when Paolo, as a true showman, was the life and soul of the company with his pleasantness and his skill as a piano player; or the football games played on Saturday in a small pitch on one of the finest hills of Naples. I always remember the days Marina and I spent at the seaside together with Paolo, Mariolina, Adriana and Giovanni, swimming in the crystal clear waters of Calabria and playing on the beach. Memories the time will never wipe out, even though life has assigned to each of us a different road to follow.

Caserta, Italy Remigio Russo

Christian Simader met Paolo Galdi for the first time in 1988, exactly 20 years ago. He describes this meeting as follows: “In the spring 1987 I was a visitor at the University of Catania in Sicily, where I gave several lectures. One was devoted to the Helmholtz decomposition of vector fields. Shortly before this visit, Hermann Sohr and I found an elementary proof of this theorem. Professor Giuseppe Mulone suggested I contact Professor Galdi from Ferrara who, at the time, was writing a book on the Navier-Stokes equations. In April 1988, my wife and I intended to participate in an intensive Italian language course at Venice. Shortly before we left for Venice, I realized that Ferrara is close to Venice, so I immediately contacted Pro- fessor Galdi who invited me to come to Ferrara. At that time I was already familiar with many of his papers, but I had never met him in person. These papers impressed me deeply because of their clearness, accuracy and profoundness. Therefore, I had the impression that the author had to be a mature mathematician, much older than I was. Our first appointment was in a hotel in Ferrara. Precisely at the time of our appointment, a young couple entered the lounge and was obviously looking for someone. After some seconds, I asked the man if he was Professor Galdi. He said yes and I introduced my wife and myself. He was very surprised Ð and told me that he thought vice versa that I had to be much older. From his mathematical studies with Professor Carlo Miranda at Naples, he knew my old Springer Lecture Notes from 1972 which in fact was an English translation (at least I regarded it so) of my thesis from 1968. So we laughed a lot and spent a very nice evening together, enjoy- ing a wonderful dinner. My wife and I had the impression of a very sympathetic and