P
Patrick Gérard
Researcher at Département de Mathématiques
Publications - 66
Citations - 5231
Patrick Gérard is an academic researcher from Département de Mathématiques. The author has contributed to research in topics: Sobolev space & Nonlinear Schrödinger equation. The author has an hindex of 29, co-authored 65 publications receiving 4867 citations. Previous affiliations of Patrick Gérard include University of Paris-Sud & University of Paris.
Papers
More filters
Journal ArticleDOI
Homogenization limits and Wigner transforms
TL;DR: In this article, the authors present a theory for carrying out homogenization limits for quadratic functions (called energy densities) of solutions of initial value problems (IVPs) with anti-self-adjoint (spatial) pseudo-differential operators (PDOs).
Journal ArticleDOI
High frequency approximation of solutions to critical nonlinear wave equations
Hajer Bahouri,Patrick Gérard +1 more
TL;DR: In this paper, the authors describe bounded energy sequences of solutions to the linear wave equation (1) in terms of their energy, up to remainder terms small in energy norm and in every Strichartz norm.
Journal ArticleDOI
Microlocal defect measures
TL;DR: In this paper, weak continuity of quadratic forms on spaces of L 2 solutions of systems of partial differential equations is studied. But defect measures on the space of positions and frequencies are not defined.
Journal ArticleDOI
Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds
TL;DR: In this article, Strichartz estimates with fractional loss of derivatives for the Schrodinger equation on any Riemannian compact manifold were shown to have low regularity local well-posedness results in any dimension.