Who was Jean Jacques Moreau?

Jean Jacques Moreau was born in Blayes in 1923. Between a scientific mother and a philosophical father, a member of the Academy of Moral and Political Sciences, he proved to be an extraordinary student, a great lover of intellectual freedom, which he would remain for the rest of his life. He chooses the scientific path precisely in order to be free, the freedom that hypersensitive intelligences need. Experimental exploration interested him and he was full of ideas for technological devices. But he renounced it because, he said, "the director of an experimental team is condemned to seek fundings". Always this thirst for freedom. He therefore turned to Theoretical Mechanics.

A graduate in Mathematics and a docteur d'Etat, Jean Jacques Moreau began his career in Poitiers and then moved to Montpellier where he became a Professor in 1953. He will not leave this city until his death in 2014.

Among J. J. Moreau's many contributions, three deserve special mention: the discovery of helicity and its conservation in non-viscous fluids, the foundation of convex analysis in infinite dimension, and the so-called non-regular, or "non-smooth" mechanics. Each of these contributions has paved the way for flourishing areas that are still in full development.

Helicity: It is not common for a scientist to have the chance to discover a conservation law in nature. Helicity is the vorticity projected on the velocity of the fluid and J. J. Moreau showed with great elegance that this quantity integrated on a patch (which he called islet), is preserved along the Lagrangian path of the patch in the fluid, in the absence of viscous dissipation. This is a very strong remark, in the same vein as Leray's demonstration of the impossibility of a singularity in two-dimensional viscous flows since it constrains the possible results in a particular situation by a rigorous limit. J. J. Moreau provided for the conservation of helicity, which can be considered as an integral version of Kelvin's circulation theorem.

Convex Analysis: Among the many problems that J. J. Moreau has addressed in fluid mechanics, cavitation, which he had formulated as a unilateral problem, provided him with the motivation to address more general unilateral problems: "The study of dynamic problems for finite or infinite systems of freedom with unilateral constraints (for example, the beginning of cavitation in a perfect incompressible fluid) first motivated the author's involvement in the development of the theory of convexity. »

A general mathematical framework was missing to describe very strong non-linearities, whose unilateral problems are an emblematic example, at least for systems with infinite degrees of freedom. Thus, instead of following a general trend which he finds regrettable, "traditional physics almost always starts from linear laws as first approximations to which improvements may have to be added taking into account higher order terms", he rather constructed by himself all the mathematics necessary to attack unilateral problems without compromising on non-linearity. This was the origin of his pioneering contribution to Convex Analysis, a field where his name is on the same footing as that of Werner Fenchel and Ralph Tyrell Rockafellar. Fenchel-Moreau's theorem (on bipolar functions), and the "proximal function" (or Moreau-Yosida regularization) and more generally his famous course at the Collège de France which he gave at the invitation of Jean Leray are some examples of the lasting impact he has had on the subject.

In addition to his interest in mathematical constructions, illustrated in his contribution to Convex Analysis, J. J. Moreau has never lost sight of mechanics. At the beginning of the 1970s he formulated the quasi-static evolution problem of elasto-plastic bodies in the form of a highly non-linear evolution equation that he called "sweeping by a moving convex set".  He then forged new mathematical and numerical tools, obtaining the first proof of existence and uniqueness for the history of stresses in an elasto-plastic material.

Non-regular dynamics: Since the early 1980s, J.J. Moreau has focused on non-smooth dynamics, avoiding any type of regularization in accordance with his vision of physics. To this end, he wrote the equations of dynamics in the presence of shocks using velocity fields with bounded variations, without explicit use of acceleration.

Retired in 1985, he developed his own computational codes. In 1986 the Academy of Sciences awarded him the Joanidès Prize with which he acquired a personal computer with which he would jubilantly perform simulations and numerical experiments on granular materials and more generally discrete systems in frictional contact, his new passion. His rigorous algorithms for unilateral problems and friction, without regularization or penalization artifacts, worked wonderfully. Its pioneering simulations were quite appealing to experimentalists whose experiments were thus reproduced and explained, including the most confusing ones.

It is quite remarkable, and relatively rare, that the scientific work of the same person has an impact in such diverse fields. The Journal of Convex Analysis and the Comptes Rendus Mécanique have each published a special issue that gives an idea of the current state of this great scientist's ideas.

Publication_list_Jean_Jacques_Moreau.pdf

Special issue of Journal of Convex Analysis dedicated to Jean Jacques Moreau

Special issue of Comptes Rendus Mécanique dedicated to Jean Jacques Moreau