### Walter Strauss

## Biography

Ph.D., Massachusetts Institute of Technology, 1962

Nonlinear waves are ubiquitous throughout the natural world. Some examples are ocean waves, the solar wind, vibrational waves in materials and laser beams. These disparate kinds of phenomena can be described by mathematical models that are based on hyperbolic, elliptic and dispersive partial differential equations and that are surprisingly similar to each other. My research is devoted to understanding the fundamental underlying features of these models and their relationships to the physical phenomena. When I began my research, most kinds of nonlinear waves were extremely poorly understood but in recent years tremendous advances have been made by many people. Some specific topics that I have studied are scattering theory in electromagnetism and acoustics, stability of waves, relativistic Yang-Mills theory, kinetic theory of plasmas, theory of fluids, and water waves.

**Biography**

Professor Strauss received a Ph.D. in Mathematics from M.I.T. in 1962. After an N.S.F. postdoctoral fellowship at the University of Paris and three years at Stanford University, he joined the Department of Mathematics at Brown in 1966. Subsequently he also joined the Division of Applied Mathematics. He chaired the Department of Mathematics during the periods 1989-1992 and 2000-2001. He has received Fulbright and Guggenheim fellowships and an Institut Henri Poincare Prize. He has visited, for a semester or more, each of the following: C.U.N.Y., U. of Paris, University of Tokyo, M.I.T., University of Maryland, Yunnan University, Courant Institute (NYU), University of Houston, Inst. H. Poincare (Paris), Duke University and the Mittag-Leffler Institute (Sweden). Since 2000 he has been the Editor-in-Chief of the SIAM Journal on Mathematical Analysis. Strauss is the author of more than 100 research articles and two books. The main focus of his research has been the analysis of nonlinear waves. They are modeled by hyperbolic, elliptic or dispersive partial differential equations. Some of his specific research areas have been scattering theory in electromagnetism and acoustics, stability of waves, relativistic Yang-Mills theory, kinetic theory of plasmas, theory of fluids, and water waves.

**Research Interests**

One of my current research projects is the study of water waves with vorticity. This is a free-boundary problem because the water surface is an unknown. Vorticity indicates the presence of eddies in the water. I study exact waves modeled by the Euler equations without assuming shallow water or small-amplitude approximations. Recently I have proven the existence of many continua of large-amplitude water waves. Some questions under current study include the location of stagnation points, stability properties of the waves, periodic and solitary waves, numerical computation of the waves, and the occurrence of overhanging waves.

Another focus of my research is the instabilities of plasmas for which collisions are rare. Such plasmas occur in various astrophysics phenomena and in hot nuclear reactors. Despite a huge amount of research over several decades, precise analyses of instabilities have been made only in very special situations. The usual model is the coupled Vlasov and Maxwell equations. There are many equilibria, including homogeneous ones, electric ones and magnetic ones. I am developing new general criteria for their stability.

Some other specific areas of my research include the stability of equilibria in semiconductor models, waves in hyperelastic materials, the scattering of fourth-order waves, and the interactions of nonlinear and spatial effects in wave models.

**Affiliations**

Editor-in-Chief: SIAM Journal on Mathematical Analysis.

Member of Editorial Boards of: J. of Differential Equations, Applied and Computational Mathematics, Dynamics and Differential Equations, Discrete and Continuous Dynamical Systems, Communications on Applied Nonlinear Analysis, SIAM J. of Mathematical Analysis, CRC Monographs in Pure & Applied Mathematics.

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## Awards

NSF Postdoctoral Fellowship, Université de Paris, 1962-63.

Fulbright Lecturer, I. M. P. A., Rio de Janeiro, 1967.

John Simon Guggenheim Fellow, 1971.

Fellow of the Japan Society for Promotion of Science, University of Tokyo, 1972.

Principal Lecturer, Conf. Bd. of Math. Sciences, A.M.S., 1989.

Harrison S. Kravis University, Professor, Brown University, 1993-94.

L. Herbert Ballou University Professor, Brown University, 1995 - present.

Institut Henri Poincaré Gauthiers-Villars Prize 1997.

Thomson-ISI New Hot Paper in Mathematics 2005.