2 citations · 2 across the 8 of their papers we have counts for
6 papers · 1 filter
Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus
Nicolas Burq, Pierre Germain, Massimo Sorella +1
We investigate trace and observability inequalities for Laplace eigenfunctions on the d-dimensional torus, with respect to arbitrary Borel measures . Specifically, we characteri…
Local Wellposedness and Global Weak Solutions of the Pauli-Darwin/Poisswell Equations
Pierre Germain, Norbert J. Mauser, Jakob Möller
We construct local (in time) strong solutions in {, } and global weak solutions with finite energy for both the Pauli-Darwin and the Pauli-Poisswell syste…
On the vanishing of eigenfunctions of the Laplacian on tori
Pierre Germain, Iván Moyano, Hui Zhu
Consider an eigenfunction of the Laplacian on a torus. How small can its -norm be on small balls? We provide partial answers to this question by exploiting the distribution of…
On the stability of the Abrikosov lattice in the Lowest Landau Level
Pierre Germain, Valentin Schwinte, Laurent Thomann
We study the Lowest Landau Level equation set on simply and doubly-periodic domains (in other words, rectangles and strips with appropriate boundary conditions). To begin with, we…
On universality for the kinetic wave equation
Pierre Germain, Hui Zhu
On compact Riemannian manifolds with chaotic geometries, specifically those exhibiting the random wave model conjectured by Berry, we derive heuristically a homogeneous kinetic wav…
Global Solutions for the Gravity Water Waves Equation in Dimension 3
P. Germain, N. Masmoudi, J. Shatah
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L^…