3 citations · 10 across the 9 of their papers we have counts for
9 papers
Energy cascades and condensation via coherent dynamics in Hamiltonian systems
Anxo Biasi, Patrick Gérard
This work makes analytic progress in the deterministic study of turbulence in Hamiltonian systems by identifying two types of energy cascade solutions and the corresponding large-…
Global Well-Posedness and Soliton Resolution for the Half-Wave Maps Equation with Rational Data
Patrick Gérard, Enno Lenzmann
We study the energy-critical half-wave maps equation: \[ \partial_t \mathbf{u} = \mathbf{u} \times |D| \mathbf{u} \] for . O…
The Benjamin-Ono equation in the zero-dispersion limit for rational initial data: generation of dispersive shock waves
Elliot Blackstone, Louise Gassot, Patrick Gérard +1
The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in is obtained explicitly for generic rati…
The Benjamin-Ono Initial-Value Problem for Rational Data with Application to Long-Time Asymptotics and Scattering
Elliot Blackstone, Louise Gassot, Patrick Gérard +1
We show that the initial-value problem for the Benjamin-Ono equation on with rational initial data with only simple poles can be solved in closed for…
A Nekhoroshev theorem for some perturbations of the Benjamin-Ono equation with initial data close to finite gap tori
Dario Bambusi, Patrick Gérard
We consider a perturbation of the Benjamin Ono equation with periodic boundary conditions on a segment. We consider the case where the perturbation is Hamiltonian and the correspon…
On the low regularity phase space of the Benjamin-Ono equation
Patrick Gérard, Peter Topalov
In this paper we prove that the Benjamin-Ono equation is globally in time -well-posed in the Hilbert space of periodic distributi…
The zero dispersion limit for the Benjamin--Ono equation on the line
Patrick Gérard
We identify the zero dispersion limit of a solution of the Benjamin--Ono equation on the line corresponding to every initial datum in . We infer a maximu…
The cubic Szegő equation on the real line: explicit formula and well-posedness on the Hardy class
Patrick Gérard, Alexander Pushnitski
We establish an explicit formula for the solution of the the cubic Szegő equation on the real line. Using this formula, we prove that the evolution flow of this equation can be con…
An inverse spectral problem for non-compact Hankel operators with simple spectrum
Patrick Gérard, Alexander Pushnitski, Sergei Treil
We consider an inverse spectral problem for a class of non-compact Hankel operators such that the modulus of (restricted onto the orthogonal complement to its kernel) has s…