Geneviève Raugel (27 May 1951 – 10 May 2019) was a French mathematician working in the field of numerical analysis and dynamical systems.[1]
Biography
Raugel entered the École normale supérieure de Fontenay-aux-Roses in 1972, obtaining the agrégation in mathematics in 1976. She earned her Ph.D degree from University of Rennes 1 in 1978 with a thesis entitled Résolution numérique de problèmes elliptiques dans des domaines avec coins (Numerical resolution of elliptic problems in domains with edges).
Raugel got a tenured position in the CNRS the same year, first as a researcher (1978–1994) then as a research director (exceptional class from 2014 on). Beginning in 1989, she worked at the Orsay Math Lab of CNRS affiliated to the University of Paris-Sud since 1989.[2]
She co-directed the international Journal of Dynamics and Differential Equations from 2005 on.[4]
Research
Raugel's first research works were devoted to numerical analysis, in particular finite element discretization of partial differential equations. With Christine Bernardi, she studied a finite element for the Stokes problem, now known as the Bernardi-Fortin-Raugel element.[5] She was also interested in problems of bifurcation, showing for instance how to use invariance properties of the dihedral group in these questions.
In the mid-1980s, she started working on the dynamics of evolution equations, in particular on global attractors,[6]perturbation theory, and the Navier-Stokes equations in thin domains.[7] In the last topic she was recognized as a world expert.[2]
Selected publications
with Christine Bernardi, Approximation numérique de certaines équations paraboliques non linéaires, RAIRO Anal. Numér. 18, 1984–3, 237–285.
with Jack Hale: Reaction-diffusion equation on thin domains, Journal de mathématiques pures et appliquées 71, 1992, 33–95.
with Jack Hale: Convergence in gradient-like systems with applications to PDE, Z. Angew. Math. Phys. 43, 1992, 63–124.
Dynamics of Partial Differential Equations on Thin Domains, in: R. Johnson (ed.), Dynamical systems. Lectures given at the Second C.I.M.E. (Montecatini Terme, Juni 1994), Lecture Notes in Mathematics 1609, Springer 1995, S. 208–315
with Jerrold Marsden, Tudor Ratiu: The Euler equations on thin domains, International Conference on Differential Equations (Berlin, 1999), World Scientific, 2000, 1198–1203
with Klaus Kirchgässner: Stability of Fronts for a KPP-system: The noncritical case, in: Gerhard Dangelmayr, Bernold Fiedler, Klaus Kirchgässner, Alexander Mielke (eds.), Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability, Longman, Harlow 1996, 147–209; part 2 (The critical case): J. Differential Equations, 146, 1998, S. 399–456.
Global Attractors in Partial Differential Equations, Handbook of Dynamical Systems, Elsevier, 2002, p. 885–982.
with Jack Hale: Regularity, determining modes and Galerkin methods, J. Math. Pures Appl., 82, 2003, 1075–1136.
with Romain Joly: A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations, Confluentes Math., 3, 2011, 471–493, Arxiv
with Marcus Paicu: Anisotropic Navier-Stokes equations in a bounded cylindrical domain, in: Partial differential equations and fluid mechanics, London Math. Soc. Lecture Note Ser., 364, Cambridge Univ. Press, 2009, 146–184, Arxiv
with Romain Joly: Generic Morse-Smale property for the parabolic equation on the circle, Transactions of the AMS, 362, 2010, 5189–5211, Arxiv
with Jack Hale: Persistence of periodic orbits for perturbed dissipative dynamical systems, in: Infinite dimensional dynamical systems, Fields Institute Commun., 64, Springer, New York, 2013, 1–55.
^R. Glowinski et J. Xu, eds., Numerical Methods for Non-Newtonian Fluids, Handbook of Numerical Analysis, vol. 16, Elsevier, 2010, p. 49-50.
^G. Raugel, Global Attractors in Partial Differential Equations, Handbook of Dynamical Systems, Elsevier, 2002, p. 885–982.
^G. Raugel et G. R. Sell, Navier-Stokes Equations on Thin 3D Domains. I: Global Attractors and Global Regularity of Solutions, Journal of the American Mathematical Society 6 (3), 503–568.
.jpg)
