Aller au contenu  Aller au menu  Aller à la recherche

Bienvenue - Laboratoire Jacques-Louis Lions

Print this page |
1) LPPR/retraites : Le Laboratoire Jacques Louis Lions soutient la motion du CoNRS ( (suite...)

Plusieurs postes ouverts au recrutement au Laboratoire Jacques-Louis Lions

Attention postes au fil de l’eau Date limite de candidature : jeudi 5 mars 2020 à 16h

Lien vers les postes


Chiffres clefs

189 personnes travaillent au LJLL

90 permanents

82 chercheurs et enseignants-chercheurs permanents

8 ingénieurs, techniciens et personnels administratifs

99 personnels non permanents

73 doctorants

14 post-doc et ATER

12 émérites et collaborateurs bénévoles


Chiffres mars 2019


2018-GdT ITER - N. Besse

Mardi 13 Mars 2018 à 11h en 15-16-413 : Nicolas Besse (Observatoire de Nice)

Regularity of the geodesic flow of the incompressible Euler equations on a manifold

In this talk we investigate the time regularity of the volume-preserving geodesic flow, which is associated to the incompressible Euler equations on a compact d-dimensional Riemannian manifold with boundary.
Not only the global regularity for smooth initial data is an open issue, but the behaviour of solutions and many pratical applications also depend on complex geometries. Our result completes the local-in-time well-posedness theory of Ebin and Marsden (Ann. Math. 92 (1970) 102–163).
Indeed, the first result of this talk states roughly that the time smoothness of geodesic curves is only limited by the smoothness of the manifold and its boundary, which is measured in a broad ultradifferentiable class, including the real analytic class.
A second result is that our simple constructive proof can be used to design efficient and very high-order semi-Lagrangian methods for integrating accurately the Euler equations on a manifold. Indeed, the proof makes use of a new Lagrangian formulation of Euler equations on d-dimensional manifolds, which is a generalization of the Cauchy invariants equation in R^3. This Lagrangian formulation, together with the Lagrangian incompressibility condition and the invariance of the boundary under the Lagrangian flow allow us to derive new recursion relations among time-Taylor coefficients of the time-series expansion of the geodesic flow.