Webpage of Louise GASSOT

About

I am a CNRS researcher at IRMAR (Rennes, France).

- 2018-2021: PhD under the supervision of Patrick Gérard at the Laboratoire de Mathématiques d'Orsay (LMO).

- 2021-2022: Institute postdoc at ICERM (Brown University)

- 2022-2023: postdoc at the University of Basel with Enno Lenzmann

I am interested in the long time behavior of solutions to dispersive nonlinear PDEs. I mainly focus on PDEs with wery weak dispersion (for instance, the Schrödinger equation on the Heisenberg group) and on integrable PDEs (for instance, the Benjamin-Ono equation on the torus). Here is a lay summary of the zero-disperion limit problem for the Benjamin-Ono equation on the torus.

Here is my PhD manuscript entitled "Long-time behavior of solutions to nonlinear PDEs: orbital stability of traveling waves, dispersion, integrability, damping".

Research

Schrödinger equation on the Heisenberg group

• On the orbital stability of a family of traveling waves for the cubic Schrödinger equation on the Heisenberg group, Bulletin de la SMF, 149-1, 15--54, 2021 (arXiv, journal)

• On the radially symmetric traveling waves for the Schrödinger equation on the Heisenberg group, Pure and Applied Analysis 2-4, 739--794, 2020 (arXiv, journal)

Cauchy problem in low regularity for Schrödinger-type equations

• Pathological set with loss of regularity for nonlinear Schrödinger equations, with Rémi Carles, 2023 (arXiv)

• Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation, with Nicolas Camps and Slim Ibrahim, 2022 (arXiv)

• Pathological set of initial data for scaling-supercritical nonlinear Schrödinger equations, with Nicolas Camps, IMRN, 2022 (arXiv, journal)

• Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin operator, with Mickaël Latocca, Journal of Functional Analysis, 283--3, 2022 (arXiv, journal)

Benjamin-Ono equation on the torus

• Lax eigenvalues in the zero-dispersion limit for the Benjamin-Ono equation on the torus, to appear in SIAM Journal on Mathematical Analysis, 2023 (arXiv)

• Zero-dispersion limit for the Benjamin-Ono equation on the torus with single well initial data, Communications in Mathematical Physics, 2023 (arXiv, journal)

• Long time behavior of solutions for a damped Benjamin-Ono equation, Mathematische Zeitschrift, 300, 1939--2006, 2022 (arXiv, journal)

• The third order Benjamin-Ono equation on the torus: well-posedness, traveling waves and stability, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 38-3, 815--840, 2021 (arXiv, journal)

Proceedings

• Cubic Schrödinger half-wave equation and random initial data, with Nicolas Camps and Slim Ibrahim, Journées équations aux dérivées partielles, 2022 (pdf)

Teaching

- 2022: class « Measure - and Integration theory » at the University of Basel

- 2018-2021: teaching assistant at the mathematics department of the ENS Paris (DMA), exercices sessions to the Master 1 course « Functional analysis ».

- 2015-2018: oral exercises sessions at CPGE, an intensive undergraduate maths and physics course

I am co-author, with Thomas Blomme, Quentin Guignard and Bernard Randé, of a book of solutions to exercises given to the ENS and École Polytechnique entrance exam (at Calvage et Mounet).