18 citations · 55 across the 16 of their papers we have counts for
16 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
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 usin…
Derivation of the Higher Order Boltzmann Equation for Hard Spheres
Ioakeim Ampatzoglou, Nataša Pavlović, William Warner
In this paper we complete the program initiated by the first and second authors and rigorously derive a Boltzmann-type equation that incorporates higher order collisions among gas…
Global existence of strong solutions to the Inhomogeneous Kinetic Wave Equation
Ioakeim Ampatzoglou, 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…
Inhomogeneous wave kinetic equation and its hierarchy in polynomially weighted spaces
Ioakeim Ampatzoglou, Joseph K. Miller, Nataša Pavlović +1
Inspired by ideas stemming from the analysis of the Boltzmann equation, in this paper we expand well-posedness theory of the spatially inhomogeneous 4-wave kinetic equation, and al…
On the global in time existence and uniqueness of solutions to the Boltzmann hierarchy
Ioakeim Ampatzoglou, Joseph K. Miller, Nataša Pavlović +1
In this paper we establish the global in time existence and uniqueness of solutions to the Boltzmann hierarchy, a hierarchy of equations instrumental for the rigorous derivation of…
Moment estimates and well-posedness of the binary-ternary Boltzmann equation
Ioakeim Ampatzoglou, Irene M. Gamba, Nataša Pavlović +1
In this paper, we show generation and propagation of polynomial and exponential moments, as well as global well-posedness of the homogeneous binary-ternary Boltzmann equation. We a…
Global well-posedness and stability of the inhomogeneous kinetic wave equation near vacuum
Ioakeim Ampatzoglou
In this paper, we prove global in time existence, uniqueness and stability of mild solutions near vacuum for the 4-wave inhomogeneous kinetic wave equation, for Laplacian dispersio…
Energy estimates in sum-product and convexity problems
Akshat Mudgal
We prove a new class of low-energy decompositions which, amongst other consequences, imply that any finite set of integers may be written as , where and a…
Derivation of the kinetic wave equation for quadratic dispersive problems in the inhomogeneous setting
Ioakeim Ampatzoglou, Charles Collot, Pierre Germain
We examine the validity of the kinetic description of wave turbulence for a model quadratic equation. We focus on the space-inhomogeneous case, which had not been treated earlier;…
A Rigorous Derivation of a Boltzmann System for a Mixture of Hard-Sphere Gases
Ioakeim Ampatzoglou, Joseph K. Miller, Nataša Pavlović
In this paper, we rigorously derive a Boltzmann equation for mixtures from the many body dynamics of two types of hard sphere gases. We prove that the microscopic dynamics of two g…
Rigorous derivation of a binary-ternary Boltzmann equation for a dense gas of hard spheres
Ioakeim Ampatzoglou, Natasa Pavlovic
This paper provides the first rigorous derivation of a binary-ternary Boltzmann equation describing the kinetic properties of a dense hard-spheres gas, where particles undergo eith…
Global well-posedness of a binary-ternary Boltzmann equation
Ioakeim Ampatzoglou, Irene M. Gamba, Natasa Pavlovic +1
In this paper we show global well-posedness near vacuum for the binary-ternary Boltzmann equation. The binary-ternary Boltzmann equation provides a correction term to the classical…
Rigorous derivation of a ternary Boltzmann equation for a classical system of particles
Ioakeim Ampatzoglou, Natasa Pavlovic
In this paper, we present a rigorous derivation of a new kinetic equation describing the limiting behavior of a classical system of particles with three particle elastic instantane…
On the non-embedding of in the James Tree Space
Ioakeim Ampatzoglou
James Tree Space (), introduced by R. James, is the first Banach space constructed having non-separable conjugate and not containing . James actually proved t…