64 citations · 323 across the 21 of their papers we have counts for
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Dispersion for the Schrödinger equation inside strictly convex domains: the general case
Oana Ivanovici, Fabrice Planchon
We consider a general smooth bounded strictly convex domain of dimension and describe dispersion for the semiclassical Schrödinger equation with Dir…
Strichartz estimates for the wave equation on a 2d model convex domain
Oana Ivanovici, Gilles Lebeau, Fabrice Planchon
We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage…
Transport of gaussian measures by the flow of the nonlinear Schrödinger equation
F. Planchon, N. Tzvetkov, N. Visciglia
We prove a new smoothing type property for solutions of the 1d quintic Schrödinger equation. As a consequence, we prove that a family of natural gaussian measures are quasi-invaria…
On the growth of Sobolev norms for NLS on and manifolds
Fabrice Planchon, Nikolay Tzvetkov, Nicola Visciglia
Using suitable modified energies we study higher order Sobolev norms' growth in time for the nonlinear Schrödinger equation (NLS) on a generic or compact manifold. In $2d…
Blow-up of critical Besov norms at a potential Navier-Stokes singularity
Isabelle Gallagher, Gabriel S. Koch, Fabrice Planchon
We prove that if an initial datum to the incompressible Navier-Stokes equations in any critical Besov space , with , gives…
On the cubic NLS on 3D compact domains
Fabrice Planchon
We prove bilinear estimates for the Schrödinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the case, while on bo…