Gaspard Ohlmann

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math.AP2025

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…

math.AP2024

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…

math.AP2024

On the stability of the ill-posedness of a quasi-linear wave equation in two dimensions with initial data in $H^{7/4} (ln H^{- I^^{2}})$

Gaspard Ohlmann

This article is the continuation of \cite{ohlmann2021illposedness} where we exhibited the ill-posedness of a quasi-linear wave equation in dimension $2$ for initial data in $H^{7/4…

Scattering of Rational Solutions to the Half-Wave Maps Equation

Half-Wave Maps: Explicit Formulas for Rational Functions with Simple Poles

On the stability of the ill-posedness of a quasi-linear wave equation in two dimensions with initial data in H7/4(lnH−I^2)

On the stability of the ill-posedness of a quasi-linear wave equation in two dimensions with initial data in $H^{7/4} (ln H^{- I^^{2}})$