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8 papers · 2 filters
Partial differential systems with nonlocal nonlinearities: Generation and solutions
Margaret Beck, Anastasia Doikou, Simon J. A. Malham +1
We develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities. For arbitrary initial data, the solutions a…
Higher order expansions for the probabilistic local Cauchy theory of the cubic nonlinear Schrödinger equation on
Árpád Bényi, Tadahiro Oh, Oana Pocovnicu
We consider the cubic nonlinear Schrödinger equation (NLS) on with randomized initial data. In particular, we study an iterative approach based on a partial power se…
Morawetz estimate for linearized gravity in Schwarzschild
Lars Andersson, Pieter Blue, Jinhua Wang
The equations governing the perturbations of the Schwarzschild metric satisfy the Regge-Wheeler-Zerilli-Moncrief system. Applying the technique introduced in [2], we prove an integ…
Global well-posedness of the periodic cubic fourth order NLS in negative Sobolev spaces
Tadahiro Oh, Yuzhao Wang
We consider the Cauchy problem for the cubic fourth order nonlinear Schrödinger equation (4NLS) on the circle. In particular, we prove global well-posedness of the renormalized 4NL…
New trends in free boundary problems
Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci
We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" fea…
Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime
Lars Andersson, Pieter Blue, Jérémie Joudioux
This paper proves the existence of a bounded energy and integrated energy decay for solutions of the massless Vlasov equation in the exterior of a very slowly rotating Kerr spaceti…