13 citations · 25 across the 6 of their papers we have counts for
6 papers
Low regularity bounds for mKdV
Michael Christ, Justin Holmer, Daniel Tataru
We study the local well-posedness in the Sobolev space H^s for the modified Korteweg-de Vries (mKdV) equation on the real line. Kenig-Ponce-Vega \cite{KPV2} and Christ-Colliander-T…
Compactness in the d-bar Neumann problem, magnetic Schrodinger operators, and the Aharonov-Bohm effect
Michael Christ, Siqi Fu
Compactness of the d-bar Neumann operator is studied for weakly pseudoconvex bounded Hartogs domains in two dimensions. A nonsmooth example is constructed in which condition (P) fa…
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
Michael Christ, James Colliander, Terence Tao
In a recent paper, Kenig, Ponce and Vega study the low regularity behavior of the focusing nonlinear Schrödinger (NLS), focusing modified Korteweg-de Vries (mKdV), and complex Kort…
Absolutely continuous spectrum of Stark operators
M. Christ, A. Kiselev
We prove several new results on the absolutely continuous spectra of perturbed one-dimensional Stark operators. First, we find new classes of perturbations, characterized mainly by…
Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials
M. Christ, A. Kiselev
We prove existence of modified wave operators for one-dimensional Schrödinger equations with potential in , . If in addition the potential is conditionally integr…
Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: some optimal results
Michael Christ, Alexander Kiselev
The absolutely continuous spectrum of one-dimensional Schrödinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular,…