4 papers
On the optimal local well-posedness of the wave kinetic equation in
Ioakeim Ampatzoglou, Tristan Léger
In this paper, we give a unified treatment of the local well-posedness for the wave kinetic equation in almost critical weighted spaces with The proof…
Moment-preserving Young's inequality for the hard potential Boltzmann gain operator
Ioakeim Ampatzoglou, Tristan Léger, Tristan Léger
We prove a new moment-preserving Young's inequality for the gain operator of the Boltzmann equation with hard potentials, including the critical case of hard-spheres. Our approach…
On the ill-posedness of kinetic wave equations
Ioakeim Ampatzoglou, Tristan Léger
In this article we identify a sharp ill-posedness/well-posedness threshold for kinetic wave equations (KWE) derived from quasilinear Schrödinger models. We show well-posedness usi…
Global existence of strong solutions to the Inhomogeneous Kinetic Wave Equation
Ioakeim Ampatzoglou, Tristan Léger, Tristan Léger
In this paper we construct global dispersive solutions to the space inhomogeneous kinetic wave equation (KWE) which propagate moments and conserve mass, momentum and ene…