4 papers
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…
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…
Poisson Commuting Energies for a System of Infinitely Many Bosons
Dana Mendelson, Andrea R. Nahmod, Nataša Pavlović +2
We consider the cubic Gross-Pitaevskii (GP) hierarchy in one spatial dimension. We establish the existence of an infinite sequence of observables such that the corresponding trace…
A Rigorous Derivation of the Hamiltonian Structure for the Nonlinear Schrödinger Equation
Dana Mendelson, Andrea R. Nahmod, Nataša Pavlović +2
We consider the cubic nonlinear Schrödinger equation (NLS) in any spatial dimension, which is a well-known example of an infinite-dimensional Hamiltonian system. Inspired by the kn…