By Philippe Guyenne, Dmitry Pelinovsky, and Catherine Sulem
It is with great sadness that we convey the passing of mathematician Walter Craig on 18 January 2019, after a long and courageous battle with cancer.
Walter grew up in the San Francisco Bay Area, the son of a renowned mathematician, William Craig. He received an A.B. and M.S. in Mathematics from UC Berkeley, and a Ph.D. under the supervision of Louis Nirenberg from the Courant Institute (NYU) in 1981. He was a postdoc at CalTech then joined Stanford University before moving to Brown University in 1988. He was recruited to McMaster University in 2000 as a Tier 1 Canada Research Chair in Mathematical Analysis and its Applications. His contributions at McMaster University were recognized with conferral of the title Distinguished University Professor in 2016.
Walter was a world renowned scholar for his work on nonlinear partial diﬀerential equations, Hamiltonian dynamical systems and their applications, in particular to ﬂuid dynamics. He received numerous prestigious awards such as an Alfred P. Sloan Fellowship, an NSF Presidential Young Investigator Award and a Killam Research Fellowship. He was named a Fellow of the Royal Society of Canada in 2007, Fellow of the AAAS in 2008 and was among the inaugural class of Fellows of the AMS in 2013. He served on the editorial boards of several journals including the Philosophical Transactions of the Royal Society, the Proceedings of the AMS and the SIAM Journal on Mathematical Analysis.
Walter was a mathematical analyst with eclectic interests, who enjoyed working with colleagues from diﬀerent areas of expertise. He had an extensive scientiﬁc culture and was skillful at communicating with people from various scientiﬁc backgrounds. It was common to witness him at the center of lively conversations during seminars, conferences or workshops (and be struck by his ease to swing between English and French). He authored more than 100 research articles on topics ranging from rigorous mathematical analysis to physical modeling, numerical simulations and laboratory experiments.
One of his early papers was a seminal contribution on the well-posedness of the water-wave equations, which provided a rigorous justiﬁcation of the Korteweg–de Vries approximation in this physical context. This single-authored 200-pages long paper published in CPDE in 1985 has been a major reference in the ﬁeld of mathematical theory of water waves. Another fundamental contribution of Walter (with C.E. Wayne, CPAM 1993) concerns the application of KAM theory and Nash–Moser iterations to prove existence of periodic solutions to nonlinear wave equations. Another inﬂuential paper of him (with C. Sulem, JCP 1993) proposed a direct numerical method for solving the full water-wave equations. It is based on an elegant expansion of the Dirichlet–Neumann operator associated with the ﬂuid domain, and makes use of the fast Fourier transform to perform computations. This approach has since played a key role in the development of high-order spectral methods for simulating nonlinear water waves, widely used by oceanographers and ocean engineers.
In addition to being a brilliant researcher, Walter was a remarkable teacher and mentor who educated and supervised many students and postdocs. Many of them have gone on to become accomplished scholars.As for collaborators, he was generous with his time, support and ideas (often not hesitating to write long detailed emails to explain them). He was a constant source of inspiration, whose enthusiasm and friendship have never waned. Walter was a devoted and loving husband to Deirdre Haskell and a proud father of Zoe Haskell-Craig. He will be greatly missed by all who had the privilege of knowing him as a mathematician, colleague and dear friend.