Recent Advances in Harmonic Analysis and Partial Differential Equations: AMS Special Sessions, March 12-13, 2011, Statesboro, Georgia : the JAMI Conference, March 21-25, 2011, Baltimore, Maryland

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Andrea R. Nahmod
American Mathematical Soc., 2012 - Mathematics - 285 pages
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This volume is based on the AMS Special Session on Harmonic Analysis and Partial Differential Equations and the AMS Special Session on Nonlinear Analysis of Partial Differential Equations, both held March 12-13, 2011, at Georgia Southern University, Statesboro, Georgia, as well as the JAMI Conference on Analysis of PDEs, held March 21-25, 2011, at Johns Hopkins University, Baltimore, Maryland. These conferences all concentrated on problems of current interest in harmonic analysis and PDE, with emphasis on the interaction between them. This volume consists of invited expositions as well as research papers that address prospects of the recent significant development in the field of analysis and PDE. The central topics mainly focused on using Fourier, spectral and geometrical methods to treat wellposedness, scattering and stability problems in PDE, including dispersive type evolution equations, higher-order systems and Sobolev spaces theory that arise in aspects of mathematical physics. The study of all these problems involves state-of-the-art techniques and approaches that have been used and developed in the last decade. The interrelationship between the theory and the tools reflects the richness and deep connections between various subjects in both classical and modern analysis.
 

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Contents

The defocusing cubic nonlinear wave equation in the energysupercritical regime
1
Steins extension operator on weighted Sobolev spaces on Lipschitz domains and applications to interpolation
13
Multilinear Morawetz identities for the GrossPitaevskii hierarchy
39
Elementary Proofs for Kato Smoothing Estimates of Schrödingerlike Dispersive Equations
63
The conormal derivative problem for higher order elliptic systems with irregular coefficients
69
Localization of eigenfunctions of a onedimensional elliptic operator
99
Scattering and blow up for the twodimensional focusing quintic nonlinear Schrödinger equation
117
A numerical study
155
Time Decay for the Solutions of a FourthOrder Nonlinear Schrödinger Equation
169
Selfadjoint realizations of Schrödinger operators on vector bundles over Riemannian manifolds
175
Spectral properties of the reflection operator in two dimensions
199
Recent local and global solutions to the Lagrangian Averaged NavierStokes equation
217
Recent works on the Strauss conjecture
235
Wave operators for nonlinear wave equations with null structures
257
Fractional regularity for nonlinear Schrödinger equations with magnetic fields
271
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