3 papers
math-ph2019
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…
math-ph2019
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…
math.AP2019
The focusing energy-critical nonlinear wave equation with random initial data
Carlos Kenig, Dana Mendelson
We consider the focusing energy-critical quintic nonlinear wave equation in three dimensional Euclidean space. It is known that this equation admits a one-parameter family of radia…