i Brown University Mathematics Department

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Faculty Member

Walter Strauss

Ballou Professor Emeritus of Mathematics
and Applied Mathematics


Office: 212 Kassar House
Phone: (401) 863-7946
Fax: (401) 863-9013
Email: wstrauss<at>math.brown.edu

Mailing Address:

    Mathematics Department
    Box 1917
    Brown University
    Providence, RI 02912


Partial Differential Equations, Mathematical Physics, Stability Theory, Solitary Waves, Kinetic Theory of Plasmas, Scattering Theory, Water Waves, Dispersive Waves

SIAM Journal on Mathematical Analysis
Journal of Differential Equations
Applied and Computational Mathematics
Dynamics and Differential Equations
Discrete and Continuous Dynamical Systems
Comm. on Applied Nonlinear Analysis
CRC Monographs & Surveys in Pure & Applied Math

Department of Mathematics
Division of Applied Mathematics
Lefschetz Center for Dynamical Systems

Education: Ph.D., MIT, 1962


Nonlinear Wave Equations, NSF-CBMS Research Monograph, Amer. Math. Soc., Providence, 1989.

Partial Differential Equations: An Introduction,
Click here for a list of errata.
The Second Edition has been in print since 2008. It is strongly recommended that students use it in conjunction with the solutions manual.

Solutions Manual for: Partial Differential Equations: An Introduction, Wiley and Sons, New York, 2008, with J. Levandosky and S. Levandosky.

Recent Papers:

Stokes waves are unstable, even very small ones; dedicated to the memory of Thomas Kappeler, submitted (2024), with R. Creedon and H. Nguyen.

Proof of the transverse instability of Stokes waves, arXiv: 2312.08469 (2023), with R. Creedon and H. Nguyen.

A kinetic model of rotating galaxies; dedicated to the memory of Jean Ginibre, in: Advances in Continuous and Discrete Models, p.16 (2023) (Springer).

Modulational instability of classical water waves; dedicated to the memory of Robert Strichartz, in: From Classical Analysis to Analysis on Fractals, p.43-52 (2023) (Springer), with H. Nguyen.

Continua of steadily rotating stars; dedicated to Constantin Dafermos, Quart. Appl. Math. 81 (2023), 413-427.

Global continuation of a Vlasov model of rotating galaxies, Kin. & Rel. Models (2023) 16, 605-623, with Yilun Wu.

Existence of rotating stars with variable entropy, SIAM J. Math. Anal. 55 (2023), 2704-2739, with Juhi Jang and Yulin Wu.

Traveling water waves - the ebb and flow of two centuries, Quart. Appl. Math. 80 (2022), 317-401, with Haziot, Hur, Toland, Wahlen, Walsh and Wheeler.

Proof of modulational instability of Stokes waves in deep water, Comm. Pure Appl. Math. (2022), 1035-1084, with Huy Q. Nguyen.

Steady states of gas ionization with secondary emission, Meth. & Applics. of Anal. 29 (2022), 1-30, with Masahiro Suzuki.

Large-amplitude steady downstream water waves, Comm. Math. Phys. 387 (2021), 237-266, with A. Constantin and E. Varvaruca.

Rapidly rotating white dwarfs, Nonlinearity 33 (2020), 4783-4798, with Yilun Wu.

Large-amplitude stationary solutions of the Morrow model of gas ionization, Kinetic Rel. Mod. 12 (2019), 1297-1312, with Masahiro Suzuki.

Rapidly rotating stars, Comm. Math. Phys. 368 (2019), 701-721, with Yilun Wu.

Existence of rotating magnetic stars, Physica D 397 (2019), 65-74, with Juhi Jang and Yilun Wu.

Upper bound on the slope of steady water waves with small adverse vorticity, J. Diff. Eqns. 264 (2018), 4136-4151, with Seung Wook So.

Steady states of rotating stars and galaxies, SIAM J. Math. Anal. 49 (2017), 4865-4914, with Yilun Wu.

Global bifurcation of steady gravity water waves with critical layers, Acta Math. 217 (2016), 195-262, with A. Constantin and E. Varvaruca.

Bound on the slope of steady water waves with favorable vorticity, Arch. Rat. Mech. Anal. 222 (2016), 1555-1580, with M. Wheeler.

Global bifurcation theory for periodic traveling interfacial gravity-capillary waves with critical layers, Ann. IHP (Anal. NL) 33 (2016), 1081-1101, with D. Ambrose and D. Wright.

Convergence to equilibrium of a body moving in a kinetic sea, SIAM J. Math. Anal. 47 (2016), 4630-4651, with X. Chen.

Global magnetic confinement for the 1.5D Vlasov-Maxwell system, Kinetic \& Rel. Models 8 (2015), 153-168, with T.T. Nguyen and T. V. Nguyen.

Stationary solutions of the Vlasov-Poisson system with diffusive boundary conditions, J. Nonlin. Sci. 25 (2015), 315-342, with E. Esenturk and H. J. Hwang.

Velocity reversal criterion of a body immersed in a sea of particles, Comm. Math. Phys. 338 (2015), 139-168, with Xuwen Chen.

Approach to equilibrium of a body colliding specularly and diffusely with a sea of particles, Arch. Rat. Mech. Anal. 211 (2014), 879-910, with Xuwen Chen.

Linear stability analysis of a hot plasma in a solid torus, Arch. Rat. Mech. Anal. 211 (2014), 619-672, with T. Nguyen.

Stability analysis of collisionless plasmas with specularly reflecting boundary, SIAM J. Math. Anal. 45 (2013), 777-808, with T. Nguyen.

Vorticity jumps in steady water waves, Disc. Cont. Dyn. Sys.-B 17 (2012), 1101-1113.

Notes on stability theory, http://www.math.brown.edu/~wstrauss/StabilityTutorial2014.pdf

Periodic traveling gravity waves with discontinuous vorticity, Arch. Rat. Mech. Anal. 202 (2011), 133-175, with A. Constantin.

Steady water waves, Bull. AMS. 47 (2010), 671-694.

Transport of interfaces with surface tension by 2D viscous flows, Interfaces and Free Boundaries 12 (2010), 23-44, with D. Ambrose, M. Lopes Filho and H. Nussenzveig Lopes.

Pressure and trajectories beneath a Stokes wave, Comm. Pure Appl. Math. 63 (2010), 533-557, with A. Constantin.

Analyticity of the scattering operator for fourth-order nonlinear waves, Disc. Cont. Dyn. Sys. 25 (2009), 617-625, with B. Pausader.

Trochoidal solutions to the incompressible two-dimensional Euler equations, J. Math. Fluid Mech. 12 (2010), 181-201, with A. Constantin.

Effect of vorticity on steady water waves, J. Fluid Mech. 608 (2008), 197-215, with J. Ko.

A sharp stability criterion for the Vlasov-Maxwell system, Inventiones Math. 173 (2008), 497-546, with Z. Lin.

Large-amplitude steady rotational water waves, Eur. J. Mech. B Fluids 27 (2008), 96-109, with J. Ko.

Instability of steady states for nonlinear wave and heat equations, J. Diff. Eqns. 241 (2007), 184-205, with P. Karageorgis.

Rotational steady water waves near stagnation, Phil. Trans. Roy. Soc. 365 (2007), 2227-2239, with A. Constantin.

Stability properties of steady water waves with vorticity, Comm. Pure Appl. Math. 60 (2007), 911-950, with A. Constantin.

Linear stability and instability of relativistic Vlasov-Maxwell systems, Comm. Pure Appl. Math. 60 (2007), 724-787, with Zhiwu Lin.

Nonlinear stability and instability of relativistic Vlasov-Maxwell systems, Comm. Pure Appl. Math. 60 (2007), 789-837, with Zhiwu Lin.

Variational formulations of steady water waves with vorticity, J. Fluid Mech. 548 (2006), 151-163, with A. Constantin and D. Sattinger.

Stability of semiconductor states with insulating and contact boundary conditions, Arch. Rat. Mech. Anal. 179 (2005), 1-30, with Y. Guo.

Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math. 57 (2004), 481-527, with A. Constantin.

Nonlinear instability of dispersive waves, in: T. Kato's method and principle for evolution equations in math. physics, Yurinsha, Tokyo (2002), 173-178.

Exact periodic traveling waves with vorticity, C. R. Acad. Sci. Paris 335 (2002), 797-800. with A. Constantin.

Irving Segal's work in partial differential equations, J. Funct. Anal. 190 (2002), 25-28 (in memory of I. E. Segal).

Stable and unstable ideal plane flows, Chinese Annals Math. 23B (2002), 149-164, with C. Bardos and Y. Guo (in memory of J. L. Lions).

Instability of traveling waves of the Kuramoto-Sivashinsky equation, Chinese Annals Math. 23B (2002), 267-276, with Guanxiang Wang (in memory of J. L. Lions).

Stability of the Camassa-Holm solitons, J. Nonlin. Sci. 12 (2002), 415-422, with A. Constantin.

Time decay for the nonlinear beam equation, Meth. & Applics. of Analysis 7 (2001), 479-488, with S. Levandosky (dedicated to C. S. Morawetz).

Magnetically created instability in a collisionless plasma, J. de Maths. Pures et Appliq. 79, 10 (2000), 975-1009, with Y. Guo.

Stability of a class of solitary waves in elastic compressible rods, Phys. Lett. A 270 (2000), 140-148, with A. Constantin.

Regular solutions of the Vlasov-Poisson-Fokker-Planck system, Discrete & Cont. Dyn. Sys. 6 (2000), 751-772, with K. Ono.

Stability of peakons, Comm. Pure Appl. Math. 53 (2000), 603-610, with A. Constantin.

Spectral condition for instability, Contemp. Math. 255 (2000), 189-198, with J. Shatah.

An inhomogeneous boundary value problem for nonlinear Schrodinger equations, J. Diff. Eqns. 173 (2001), 79-91, with C. Bu.

Perturbation of essential spectra of evolution operators and the Vlasov- Poisson-Boltzmann system, Discrete & Cont. Dyn. Sys. 5 (1999), 457-472, with R. Glassey.

Robustness of instability for the two-dimensional Euler equations, SIAM J. Math. Anal. 30 (1999), 1343-1354, with S. Friedlander and M. Vishik.

Unstable oscillatory-tail waves in collisionless plasmas, SIAM J. Math. Anal. 30 (1999), 1076-1114, with Y. Guo.

Decay of the linearized Boltzmann-Vlasov system, Trans. Th. Stat. Phys. 28, 135-156, with R. Glassey.

Stability and instability in the kinetic theory of plasmas, Mathemática Contemporanêa 15 (1999), 249-258.

Relativistic unstable periodic BGK waves, Comput. and Appl. Math. 18 (1999), 87-122, with Y. Guo.

Unstable BGK solitary waves and collisionless shocks, Comm. Math. Phys. 195 (1998), 267-293, with Y. Guo.

Existence and blow up of small-amplitude nonlinear waves with a negative potential, Discrete & Cont. Dyn. Sys. 3 (1997), 175-188, with K. Tsutaya.

Stability, instability and regularity of nonlinear waves, in: Nonlinear Waves, T. Ozawa, ed., Gakuto Int'l Series, Gakkotosho, Tokyo, 1997, p. 451-468.

Breathers as homoclinic geometric wave maps, Physica D 99 (1996), 113-133, with J. Shatah.

Nonlinear instability in an ideal fluid, Annales de l'IHP (Anal. NL) 14 (1997), 187-209, with S. Friedlander and M. Vishik.

The relativistic Boltzmann equation, in: Quantization, Nonlinear PDEs and Operator Algebras, W. Arveson et al., eds., P.S.P.M. 59 (1996), Amer. Math. Soc., p. 203-209.

Microlocal dispersive smoothing for the Schrodinger equation, Comm. Pure Appl. Math. 48 (1995), 769-860, with W. Craig and T. Kappeler.

Instability of periodic BGK equilibria, Comm. Pure Appl. Math. 48 (1995), 861-894, with Y. Guo.

Global finite-energy solutions of the Maxwell-Schrodinger system, Comm. Math. Phys. 170 (1995), 181-196, with Y. Guo and K. Nakamitsu.

Asymptotic stability of the relativistic maxwellian via fourteen moments, Transport Th. Stat. Phys. 24 (1995), 657-678, with R. Glassey.

Ph.D. Students:
Charles Harvey
Rodney Johnson
Robert Glassey
David Costa
Gustavo Perla Menzala
Jeng-Eng Lin
Clayton Keller
Jalal Shatah
Musheng Wei
Manoussos Grillakis
Brian Loe
Yan Guo
Yue Liu
Steven Levandosky
Julie Benson Levandosky
Zhiwu Lin
Pete Karageorgis
Vera Mikyoung Hur
Robin Ming Chen
Samuel Walsh
Jonathan Ben-Artzi
Miles Wheeler
Zhiyuan Zhang

Last modified September 2019