147 citations · 1.7k across the 86 of their papers we have counts for
5 papers · 1 filter
A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces
Herbert Koch, Daniel Tataru
We consider the cubic Nonlinear Schrodinger Equation in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time H^s bounds in…
Wave packet parametrices for evolutions governed by PDO's with rough symbols
Jeremy Marzuola, Jason Metcalfe, Daniel Tataru
In this note, we consider wave packet parametrices for Schrodinger-like evolution equations. Under an integrability condition along the flow, we prove that the flow is then globall…
Renormalization and blow up for charge one equivariant critical wave maps
Joachim Krieger, Wilhelm Schlag, Daniel Tataru
We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically res…
Large data local solutions for the derivative NLS equation
Ioan Bejenaru, Daniel Tataru
We consider the Derivative NLS equation with general quadratic nonlinearities. In \cite{be2} the first author has proved a sharp small data local well-posedness result in Sobolev s…
Semiclassical Lp estimates
Herbert Koch, Daniel Tataru, Maciej Zworski
The purpose of this paper is to use semiclassical analysis to unify and generalize Lp estimates on high energy eigenfunctions and spectral clusters. In our approach these estimates…