695 citations
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6 papers · 1 filter
Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions
Jason Metcalfe, Ann Stewart
In this paper, we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with Neumann bou…
The initial-boundary value problem for the Korteweg-de Vries equation
Justin Holmer
We prove local well-posedness of the initial-boundary value problem for the Korteweg-de Vries equation on the right half-line, left half-line, and line segment, in the low regulari…
Dispersive estimates for principally normal pseudodifferential operators
Herbert Koch, Daniel Tataru
The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes fr…
Instability of the periodic nonlinear Schrodinger equation
Michael Christ, James Colliander, Terence Tao
We study the periodic non-linear Schrodinger equations with odd integer power nonlinearities, for initial data which are assumed to be small in some negative order Sobolev space, b…
Ill-posedness for nonlinear Schrodinger and wave equations
Michael Christ, James Colliander, Terence Tao
The nonlinear wave and Schrodinger equations on Euclidean space of any dimension, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be…
Quantum resonances and partial differential equations
Maciej Zworski
Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, t…