596 citations · 795 across the 25 of their papers we have counts for
5 papers · 1 filter
Global well-posedness, scattering and blow-up for the energy critical focusing non-linear wave equation
Carlos E. Kenig, Frank Merle
We prove, for the energy critcal, focusing NLW, that for Cauchy data (u_0, u_1) whose energy is smaller than that of (W,0), where W is the well-known radial positive solution to th…
Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
Carlos E. Kenig, Frank Merle
We prove, for the energy critical, focusing NLS, that for data whose energy is smaller than that of the standing wave, and whose homogeneous Sobolev norm H^1 is smaller than that o…
Global existence and uniqueness of Schrödinger maps in dimensions
I. Bejenaru, A. D. Ionescu, C. E. Kenig
In dimensions , we prove that the Schrödinger map initial-value problem admits global (in time) solutions for smooth data with small norm in the critical Sobolev space.
On uniqueness properties of solutions of the k-generalized KdV equations
Luis Escauriaza, Carlos E. Kenig, Gustavo Ponce +1
In this paper we study uniqueness properties of solutions of the k-generalized Korteweg-de Vries equation. Our goal is to obtain sufficient conditions on the behavior of the differ…
Determining a magnetic Schroedinger operator from partial Cauchy data
David Dos Santos Ferreira, Carlos Kenig, Johannes Sjoestrand +1
In this paper we show, in dimension n >=3, that knowledge of the Cauchy data for the Schroedinger equation in the presence of a magnetic potential, measured on possibly very small…