7 citations · 9 across the 5 of their papers we have counts for
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Dynamics of nonlinear Klein-Gordon equations in low regularity on S^2
Joackim Bernier, Benoît Grébert, Gabriel Rivière
We describe the long time behavior of small non-smooth solutions to the nonlinear Klein-Gordon equations on the sphere S^2. More precisely, we prove that the low harmonic energies…
Local norms of Schr{ö}dinger eigenfunctions on
Gabriel Rivière
On the canonical -sphere and for Schr{ö}dinger eigenfunctions, we obtain a simple geometric criterion on the potential under which we can improve, near a given point and for eve…
Equidistribution of toral eigenfunctions along hypersurfaces
Hamid Hezari, Gabriel Riviere
We prove a new quantum variance estimate for toral eigenfunctions. As an application, we show that, given any orthonormal basis of toral eigenfunctions and any smooth embedded hype…
Observability and quantum limits for the Schrödinger equation on the sphere
Fabricio Macià, Gabriel Riviere
In this note, we describe our recent results on semiclassical measures for the Schr{ö}dinger evolution on Zoll manifolds. We focus on the particular case of eigenmodes of the Schr{…
Concentration and non-concentration for the Schrödinger evolution on Zoll manifolds
Fabricio Macià, Gabriel Rivière
We study the long time dynamics of the Schrödinger equation on Zoll manifolds. We establish criteria under which the solutions of the Schrödinger equation can or cannot concentrate…
Quantitative equidistribution properties of toral eigenfunctions
Hamid Hezari, Gabriel Riviere
We prove quantitative equidistribution properties for orthonormal bases of eigenfunctions of the Laplacian on the rational -torus. We show that the rate of equidistribution of s…