Patrick Gérard

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math.AP2025

Global Well-Posedness and Soliton Resolution for the Half-Wave Maps Equation with Rational Data

Patrick GÃ©rard, Enno Lenzmann

We study the energy-critical half-wave maps equation: \[ \partial_t \mathbf{u} = \mathbf{u} \times |D| \mathbf{u} \] for $u : [0, T) \times R \to S^{2}$ . O…

math.AP2025

The Benjamin-Ono Initial-Value Problem for Rational Data with Application to Long-Time Asymptotics and Scattering

Elliot Blackstone, Louise Gassot, Patrick GÃ©rard +1

We show that the initial-value problem for the Benjamin-Ono equation on $R$ with $L^{2} (R)$ rational initial data with only simple poles can be solved in closed for…

math.AP2024

The Benjamin-Ono equation in the zero-dispersion limit for rational initial data: generation of dispersive shock waves

The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in $L^{2} (R)$ is obtained explicitly for generic rati…