Journal of Dynamics and Differential Equations (2021) 33:1175–1177 https://doi.org/10.1007/s10884-021-10039-9
Preface to the Special Issue in Memory of Walter Craig
© Springer Science+Business Media, LLC, part of Springer Nature 2021
More than two years have gone since Professor Walter Craig passed away on January 18, 2019, and the loss continues to be felt deeply by his relatives, friends, and colleagues.
With contributions from a group of invited authors in Hamiltonian dynamics and nonlinear PDEs in which Walter had long worked, this Special Issue of the Journal of Dynamics and Differential Equations is made in his memory. We also would like to dedicate this Special Issue to acknowledge his many valuable services to this journal as a member of the editorial board for many years.
The son of a renowned mathematician, William Craig, Walter graduated with an A.B.
degree in Mathematics from UC Berkeley in 1977. He earned a Ph.D. degree in 1981 in Mathematics at the Courant Institute, NYU, under the supervision of Louis Nirenberg. After postdoctoral work at CalTech, he worked at Stanford and Brown Universities for many years before moving to McMaster University in 2000 as a Canada Research Chair in Mathemati- cal Analysis and its Applications. His professional accomplishments and contribution to the international mathematical society were acknowledged with a variety of academic distinc- tions, among which are fellows of the Royal Society of Canada, the American Association for the Advancement of Science, and the American Mathematical Society, an Alfred P. Sloan Fellowship, an NSF Presidential Young Investigator Award, and a Killiam Fellowship. In addition he was named a Distinguished University Professor at McMaster University.
Walter was a world renowned leader in the fields of nonlinear partial differential equa- tions, infinite dimensional dynamical systems, Hamiltonian systems, and their applications to water waves, general relativity, and cosmology. With over 100 publications, he had made fundamental contributions to many important areas in these fields ranging from rigorous anal- ysis of mathematical models to numerical simulations of coherent structures and nonlinear waves.
Walter’s contribution to the Hamiltonian dynamics and KAM theory has been inspiring for many mathematicians. His paper with C.E. Wayne [Comm. Pure Appl. Math. 46 (1993), 1409–1498] concerning finding periodic solutions of nonlinear wave equations based on Newton’s method and Nash-Moser iterations is his best cited work according to MathSciNet.
The approach suggested there has been applied to other Hamiltonian PDEs in studying the existence of quasi-periodic solutions, and is now known as the Craig–Wayne method.
Walter had also made important contributions to the analysis and modeling of surface and internal water waves, including justification of the simplifying approximations of complex fluid equations, development of numerical methods for solving water-wave equations, anal- ysis of dynamics of long waves over a random bottom, and his latest work on the singularity set in the three-dimensional Navier–Stokes equations.
Walter performed distinguished services for the international mathematical community.
He organized numerous conferences, workshops, and summer schools, and served on many important committees and boards of professional organizations including the AMS, AAAS,
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the Fields Institute, CRM, and PIMS. He was the director of the Lefschetz Center for Dynami- cal Systems and chair of the Department of Mathematics at Brown University each for several years, and he served as the director of the Fields Institute during the years 2013-2015. He was on the editorial boards of over ten professional journals including this one, and in fact, he committed to serve as a co-editor-in-chief of this journal before his death.
What had made Walter an admirable scholar goes far beyond his research works and professional services. He was a remarkable teacher and educator who had supervised a numerous number of students and postdocs and actually devoted tremendous amount of time working with them. As one of his postdocs had remarked, he “remembers nostalgically infinite meetings with him in cafeterias, when considerable calculations were performed on napkins, and proofs of theorems were finalized". Besides his own students and postdocs, he also inspired and helped the career developments of many young researchers working in the fields. With his broad interests in science and his exceptional communication skills with people of diversified culture and backgrounds, he had fruitful collaborations with many researchers around the world including some in very applied disciplines. Those who knew Walter always remember his gentleness, kindness, supportiveness, and positive attitude. To many of them, Walter was not just a pleasant colleague but rather a dear friend who will be severely missed.
Walter’s life, his work and memories of his friends are well presented in the Memorial Tribute "Remembrances of Walter Craig" [Notices of AMS 67(4) (2019), 520–531].
Members of the Editorial Committee:Dario Bambusi, Sergei Kuksin (Chair), Dmitry Pelinovsky, and Yingfei Yi
Co-Editors in Chief:Konstantin Mischaikow and Yingfei Yi
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Walter Craig (1953–2019)
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