About
Introduction.
I am a Postdoctoral researcher at Nantes Université, working with Joackim Bernier and Benoît Grébert. My researches focus on the study of short and long time behaviors of nonlinear dispersive PDEs both in probabilistic and deterministic settings.
My thesis called "Probabilistic approaches for nonlinear Schrödinger equations" was supervised by Nicolas Burq and Frédéric Rousset, and was defended at Orsay on September 2022.
Keywords.
Nonlinear Schrödinger equation, Probabilistic Cauchy theory, Distorted Fourier transform, Asymptotic stability, Scattering, Semiclassical analysis, Harmonic analysis, Schrödinger equation on compact manifolds.
Publications and Preprints
Cauchy theory in singular regimes
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Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation (with Slim Ibrahim and Louise Gassot)
Arxiv Preprint September 2022
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Pathological set of initial data for scaling-supercritical nonlinear Schrödinger equations (with Louise Gassot)
Arxiv Preprint March 2022, to appear in Int. Math. Res. Not. IMRN
Long time dynamics for dispersive PDEs
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Scattering for the cubic Schrödinger equation in 3D with randomized initial data,
Arxiv Preprint October 2021, to appear in Trans. Amer. Math. Soc
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Asymptotic stability of small ground states for NLS under random perturbations,
Arxiv Preprint December 2020, to appear in Ann. Inst. Henri Poincare (C) Anal. Non Lineaire
Contact
Location:
Laboratoire de Mathématiques Jean Leray, Nantes Université, 44000 Nantes, France
Office:
office 06
Email:
nicolas.camps@univ-nantes.fr