201 citations · 231 across the 16 of their papers we have counts for
20 papers
Nonlinear interpolation and the flow map for quasilinear equations
Thomas Alazard, Nicolas Burq, Mihaela Ifrim +2
We prove an interpolation theorem for nonlinear functionals defined on scales of Banach spaces that generalize Besov spaces. It applies to functionals defined only locally, requiri…
Domains of dependence for subelliptic wave equations and unique continuation for fractional powers of Hörmander's operators
Nicolas Burq, Claude Zuily
We prove the sharp domain of dependence property for solutions to subelliptic wave equations for sums of squares of vector fields satisfying Hörmander bracket condition. We deduce…
Virial theorems and equipartition of energy for water-waves
Thomas Alazard, Claude Zuily
We study several different aspects of the energy equipartition principle for water waves. We prove a virial identity that implies that the potential energy is equal, on average, to…
A remark on quantitative unique continuation from subsets of the boundary of positive measure
Nicolas Burq, Claude Zuily
The question of unique continuation of harmonic functions in a domain R d with boundary , satisfying Dirichlet boundary conditions and with normal deriva…
A note on the uniqueness from sets of positive measure for time dependent parabolic operators
Nicolas Burq, Claude Zuily
The purpose of this short note is to show how it is possible to combine existing results in the literature to get the unique continuation from sets of positive measure for time dep…
Cauchy theory for the water waves system in an analytic framework
Thomas Alazard, Nicolas Burq, Claude Zuily
In this paper we consider the Cauchy problem for gravity water waves, in a domain with a flat bottom and in arbitrary space dimension. We prove that if the data are of size $\varep…