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Scattering of Rational Solutions to the Half-Wave Maps Equation
Gaspard Ohlmann
This article studies the rational solutions of the Half-Wave Maps equation (HWM) in the non-singular spectrum case. We first provide characterizations to what we call \emph{scatter…
Half-Wave Maps: Explicit Formulas for Rational Functions with Simple Poles
Gaspard Ohlmann
We establish an explicit formula for the Half-Wave maps equation for rational functions with simple poles. The Lax pair provides a description of the evolution of the poles. By con…
On the stability of the ill-posedness of a quasi-linear wave equation in two dimensions with initial data in
Gaspard Ohlmann
This article is the continuation of \cite{ohlmann2021illposedness} where we exhibited the ill-posedness of a quasi-linear wave equation in dimension for initial data in $H^{7/4…
A Study on the Well-Posedness of 1D Energy-Critical Half-Wave Maps Equations
Gaspard Ohlmann
In this article, we study the well-posedness of the energy-critical half-wave maps equation (HWM) in dimension . The half-wave maps equation emerges from the continuum limit of…
Ill-posedness of a quasilinear wave equation in two dimensions for data in
Gaspard Ohlmann
In this article, we study the ill-posedness of a quasilinear wave equation. It was shown by Tataru and Smith in 2005 that for any (or in our situation), the equation…