4 papers
High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation
Jacek Jendrej, Tony Salvi
We investigate the global well-posedness and modified scattering for the one-dimensional Schrödinger equation with gauge-invariant polynomial nonlinearity. For small localized ini…
Semi-classical limit for Klein-Gordon equation toward relativistic Euler equations via an adapted modulated energy method
Tony Salvi
We show the convergence of the solutions to the massive nonlinear Klein-Gordon equation toward solutions to a relativistic Euler with potential type system in the semi-classical li…
Multi-phase high frequency solutions to Klein-Gordon-Maxwell equations in Lorenz gauge in (3+1) Minkowski spacetime
Tony Salvi
We study a 1-parameter family (Aλ, Φλ)λ of multi-phase high frequency solutions to Klein-Gordon-Maxwell equations in Lorenz gauge in the (3+1)-dimensional Minkowski spacetime.…
Semi-classical limit of the massive Klein-Gordon-Maxwell system toward the relativistic Euler-Maxwell system via an adapted modulated energy method
Tony Salvi
We show that the momentum, the density, and the electromagnetic field associated with the massive KleinGordon-Maxwell equations converge in the semi-classical limit towards their r…