# Robert S. Finn

Professor Robert S. Finn earned his PhD in 1951, at Syracuse University, under the supervision of Abe Gelbart. His first paper, published in 1952 on the Comptes Rendus de l’Académie des Sciences of Paris, regarded an improvement of a theorem of Picard on the eccentricity of complex functions. Shortly after that, his work, for the subsequent sixty-five years has been mostly devoted to fundamental questions related to fluid mechanics. The series of Finn’s significant contributions begins with a number of seminal articles on minimal surface equation and idealized compressible fluids, which may considered as cornerstone contributions for several generation of scholars. Particularly relevant is the resolution of a problem, proposed to him by Alexander Weinstein, concerning the motion of an idealized flow through jets, which Finn solved by using an unusual identity due to Levi-Civita. In the same paper he shows a basic error in a previous paper of H. Weyl on the same topic. Finn’s result, to date (more than fifty years later, that is), remains the best available in the field. Another not less significant contribution at that time is his joint work with D. Gilbarg, in the late 1950s, regarding 2D idealized compressible flow past an airfoil, with a further generalization to the 3D-case. It is in these papers that Finn gives the first proof of an inequality of the Sobolev type for functions having finite Dirichlet integral, which will be eventually recognized and used by many different authors as key tool in the mathematical theory of viscous flow past an obstacle. All the above research activities were developed when Professor Finn was appointed, as Assistant or Associate professor in different prestigious schools, such as IAS at Princeton, University of Maryland, USC, and Caltech. In 1959 he moved to Stanford, where he was granted Full professorship. It was around that time that he “stumbled accidentally” on Leray’s fundamental papers on the Navier-Stokes equations. We should all be thankful to this circumstance, because it was thanks to this “accident” that Finn produced his majestic contribution to the mathematical theory of viscous flow past an obstacle. In fact, he was the first to provide a complete theory of existence, uniqueness and sharp asymptotic behavior –including the presence of a wake region- for steady-state flow, in both 2- and 3-D, for small data. Particularly outstanding is the result in the 2D case, where in a seminal paper jointly with D. Smith, Finn shows that there is no Stokes paradox in the full nonlinear case. His review papers of 1965 and 1973 on the steady-state Navier-Stokes problem are unanimously considered two unquestionable landmarks of the entire mathematical fluid mechanics.

Beginning in the early 1970s, Professor Finn directs his scientific interest toward capillarity theory. Also in this discipline he produced countless fundamental contributions, also jointly with P. Concus, E. Giusti, and the late M. Shinbrot among others, which would be hopeless to detail here. We only wish to mention, for its particularly remarkable significance, the quantitative prediction of the asymptotic behavior of a capillary surface over a corner domain in a gravity field, under suitable assumption on the contact angle that Professor Finn obtained in a joint work with P. Concus. These predictions were tested and verified quantitatively in real-life configurations in a NASA drop tower and in a kitchen sink at the Stanford Medical School.

Professor Finn’s work has been recognized all over the world, also through the numerous distinguished visiting positions that he has covered all along his career in most prestigious Universities. They include the Technische Hochschule in Berlin, The Universitè de Paris, Universität Bonn, Universität Heidelberg, Scuola Normale Superiore di Pisa, Universität Leipzig, and Max-Planck Institute in Bonn. He has been Guggenheim Fellow in Berlin and Paris, in the years 1958-1959, and in Bonn, in 1965-1966; National Academy Exchange Lecturer in USSR, in 1978 and in GDR in 1987. Furthermore, Professor Finn has been awarded an Honorary Degree (Dr. Rer. Nat. Honoris Causa) by the Universität Leipzig in 1994. He is (or was) a member of the Editorial Board of several authoritative scientific forums, such as the Archive for Rational Mechanics and Analysis, Pacific Journal of Mathematics, Boundary Value Problems and Journal of Mathematical Fluid Mechanics.

The entire mathematical fluid mechanics community wishes Professor Finn many more years of great contributions, as a natural continuation of his fundamental work over the past sixty-plus years!