arXiv subjects

Tony Salvi

Publications and source records attributed to Tony Salvi.

4 recordsLinked to original sources

arXiv2026

High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schr\"odinger equation

We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we establish global existence of solution together with persistence of the localization of the associated profile. We further provide a rigorous derivation of the asymptotic expansion at arbitrary order of such solutions, taking into account long-range effects induced by the cubic component of the nonlinearity. Our analysis relies on the space-time resonance method.

math.AP↗

arXiv2025

Semi-classical limit of the massive Klein-Gordon-Maxwell system toward the relativistic Euler-Maxwell system via an adapted modulated energy method

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 respective equivalents associated with the relativistic Euler-Maxwell equations. The proof relies on a modulated stress-energy method and a compactness argument. We also give a proof of the well-posedness of the relativistic Euler-Maxwell equations and show how this system, and so the semi-classical limit of Klein-Gordon-Maxwell, is related to the relativistic massive Vlasov-Maxwell equations.

math.AP↗

arXiv2024

Semi-classical limit for Klein-Gordon equation toward relativistic Euler equations via an adapted modulated energy method

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 limit. In particular, the momentum and the density of Klein-Gordon converge to the the momentum and the density of the relativistic Euler system in Lebesgue norms. The relativistic Euler with potential is equivalent to the usual relativistic Euler with pressure up to a rescaling. The proof relies on the modulated energy method adapted to the wave equation and the relativistic setting: a modulated stress-energy method.

math.AP↗

arXiv2024

Multi-phase high frequency solutions to Klein-Gordon-Maxwell equations in Lorenz gauge in (3+1) Minkowski spacetime

We study a 1-parameter family (A{\lambda}, {\Phi}{\lambda}){\lambda} of multi-phase high frequency solutions to Klein-Gordon-Maxwell equations in Lorenz gauge in the (3+1)-dimensional Minkowski spacetime. This family is based on an initial ansatz. We prove that for {\lambda} small enough the family of solutions exists on an interval uniform in {\lambda} only function of the initial ansatz. These solutions are close to an approximate solution constructed by geometric optics. The initial ansatz needs to be regular enough, to satisfy a polarization condition and to satisfy the constraints for Maxwell null-transport in Lorenz gauge, but there is no need for smallness of any kind. The phases need to interact in a coherent way. We also observe that the limit (A0, {\Phi}0) is not solution to Klein-Gordon-Maxwell equations but to a Klein-Gordon-Maxwell null-transport type system.

math.AP↗