The first work of Temam in his thesis dealt with the fractional steps method. Thereafter, "he has continually explored and developed new directions and techniques":[2]
calculus of variations, and the notion of duality,[3] developing the mathematical framework for discontinuous (in displacement) solutions; a concept later used for his works on the mathematical theory of plasticity;[4]
mathematical formulation of the equilibrium of a plasma in a cavity, expressed as a nonlinear free boundary problem;[5]
infinite-dimensional dynamical systems theory. In particular, he studied the existence of the finite-dimensional global attractor for many dissipative equations of mathematical physics, including the incompressible Navier–Stokes equations.[9][10] He was also the co-founder of the notion of inertial manifolds[11] together with Ciprian Foias and George R. Sell and of exponential attractors[12] together with Alp Eden, Ciprian Foias and Basil Nicolaenko;[2]
optimal control of the incompressible Navier–Stokes equations as a tool for the control of turbulence;[13]
Temam's main activities concern the study of geophysical flows, the atmosphere and oceans.[2] This started in the 1990s by collaboration with Jacques-Louis Lions and Shouhong Wang.[15][16][17][18]
Of all mathematics advisors recorded by the Mathematical Genealogy Project database, Temam has the second-largest number of doctoral students.[19][20] More than 30 of his students are now full professors all over the world, and have themselves many descendants.[21]
Administrative activities
Temam became a professor at the Paris-Sud University at Orsay in 1968. There, he co-founded the Laboratory of Numerical and Functional Analysis which he directed from 1972 to 1988. He was also a Maître de Conférences at the Ecole Polytechnique in Paris from 1968 to 1986.[22]
Temam has been the Director of the Institute for Scientific Computing & Applied Mathematics (ISCAM)[26] at Indiana University since 1986 (co-director with Ciprian Foias from 1986 to 1992). He is also a College Professor (part-time till 2003) and he has been a Distinguished Professor since 2014.[27]
^R. Temam, A nonlinear eigenvalue problem: the shape at equilibrium of a confined
plasma, Arch. Rational Mech. Anal., 60, 1975, 51-73.
^R. Temam, Sur un problème non linéaire, J. Math. Pures Appl., 48, 1969, 159-172.
^B. Nicolaenko, B. Scheurer and R. Temam, Some global dynamical properties
of the Kuramoto-Sivashinsky equations: Nonlinear stability and attractors, Physica D,
16, 1985, 155-183.
^R. Temam, On the Euler equations of incompressible perfect fluids, J. Funct. Anal., 20, 1975, 32-43.
^P. Constantin, C. Foias, O. Manley and R. Temam, Determining modes and fractal dimension of turbulent flows, J. Fluid Mech., 150, 1985, 427-440.
^C. Foias, O.P. Manley and R. Temam, Physical estimates of the number of degrees of freedom in free convection, Phys. Fluids, 29, 1986, 3101-3103.
^C. Foias, G.R. Sell and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Diff. Equ., 73, 1988, 309-353.
^J.L. Lions, R. Temam and S. Wang, New formulations of the primitive equations of the atmosphere and applications, Nonlinearity, 5, 1992, 237-288.
^J.L. Lions, R. Temam and S. Wang, On the equations of the large-scale ocean, Nonlinearity, 5, 1992, 1007-1053.
^M. Coti Zelati, M. Frémond, R. Temam and J. Tribbia, Uniqueness, regularity and maximum principles for the equations of the atmosphere with humidity and saturation, Physica D, 264, 2013, 49-65, https://doi.org/10.1016/j.physd.2013.08.007
^Y. Cao, M. Hamouda, R. Temam, J. Tribbia and X. Wang, The equations of the multi-phase humid atmosphere expressed as a quasi variational inequality, Nonlinearity, 31, 2018, 4692-4723, https://doi.org/10.1088/1361-6544/aad525.
^"History of ICIAM". The International Council for Industrial and Applied Mathematics. Retrieved 10 October 2022.
^"Editorial board". ESAIM: Mathematical Modelling and Numerical Analysis. European Series in Applied and Industrial Mathematics. EDP Sciences. Retrieved 10 October 2022.
