منابع مشابه
Space-time resonances
This article is a short exposition of the space-time resonances method. It was introduced by Masmoudi, Shatah, and the author, in order to understand global existence for nonlinear dispersive equations, set in the whole space, and with small data. The idea is to combine the classical concept of resonances, with the feature of dispersive equations: wave packets propagate at a group velocity whic...
متن کاملRigged Hilbert Space Resonances and Time Asymmetric Quantum Mechanics
The Rigged Hilbert Space (RHS) theory of resonance scattering and decay is reviewed and contrasted with the standard Hilbert space (HS) theory of quantum mechanics. The main difference is in the choice of boundary conditions. Whereas the conventional theory allows for the in-states φ and the out-states (observables) ψ of the S-matrix elements (ψ, φ) = (ψout, Sφin) any elements of the HS H, {ψ} ...
متن کاملSpace-time Resonances and the Null Condition for Wave Equations
In this note we describe a recent result obtained by the author and Shatah [26], concerning global existence and scattering for small solutions of nonlinear wave equations. Based on the analysis of space-time resonances, we formulate a very natural non-resonance condition for quadratic nonlinearities that guarantees the existence of global solutions with linear asymptotic behavior. This non-res...
متن کاملResonances for Obstacles in Hyperbolic Space
We consider scattering by star-shaped obstacles in hyperbolic space and show that resonances satisfy a universal bound Imλ ≤ − 2 which is optimal in dimension 2. In odd dimensions we also show that Imλ ≤ −μρ for a universal constant μ, where ρ is the (hyperbolic) diameter of the obstacle; this gives an improvement for small obstacles. In dimensions 3 and higher the proofs follow the classical v...
متن کاملKicked rotor quantum resonances in position space
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 2009
ISSN: 0033-569X,1552-4485
DOI: 10.1090/s0033-569x-09-01175-3