Joseph Thirouin

collaborators

3 papers

math.AP2018

About the quadratic Szeg{ö} hierarchy

Joseph Thirouin

The purpose of this paper is to go further into the study of the quadratic Szeg{ö} equation, which is the following Hamiltonian PDE : $i \partial_t u = 2 J Π (∣ u ∣^{2}) + J ˉ u^{2}$ , $u(…

math.AP2018

Classification of traveling waves for a quadratic Szeg{ö} equation

Joseph Thirouin

We give a complete classification of the traveling waves of the following quadratic Szeg{ö} equation : $i \partial_t u = 2 J Π (∣ u ∣^{2}) + J ˉ u^{2}, u (0, \cdot) = u_0$ , and we sho…

math.AP2017

Optimal bounds for the growth of Sobolev norms of solutions of a quadratic Szegő equation

Joseph Thirouin

In this paper, we study a quadratic equation on the one-dimensional torus : $i \partial_{t} u = 2 J Π (∣ u ∣^{2}) + J ˉ u^{2}, u (0, \cdot) = u_{0},$ where $J=\int_\mathbb{T}|u|^2u \in\ma…