3 papers
math.AP2026
Existence of Solutions for time-dependent fractional Kohn-Sham Equations
Sébastien Breteaux, Michele Fantechi, Jérémy Faupin
We consider time-dependent Kohn-Sham equations in dimension with a fractional dispersion relation , , and a class of interaction terms including, in…
math-ph2025
Propagation Estimates for the Boson Star Equation
Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli
We consider the boson star equation with a general two-body interaction potential and initial data in a Sobolev space. Under general assumptions on , namely that …
math-ph2025
Exponential Decay outside of the Light Cone for the Pseudo-Relativistic Non-Autonomous Schrödinger Equation
Sébastien Breteaux, Jérémy Faupin, Viviana Grasselli
We establish a maximal velocity bound for a pseudo-relativistic quantum particle in an external time-dependent potential. Our estimate shows that the probability for the particle,…