29 citations · 55 across the 7 of their papers we have counts for
7 papers
On the Fourth order Schrödinger equation in three dimensions: dispersive estimates and zero energy resonances
Burak Erdogan, William R. Green, Ebru Toprak
We study the fourth order Schrödinger operator for a short range potential in three space dimensions. We provide a full classification of zero energy resonances and st…
On the Fourth order Schrödinger equation in four dimensions: dispersive estimates and zero energy resonances
William R. Green, Ebru Toprak
We study the fourth order Schrödinger operator for a decaying potential in four dimensions. In particular, we show that the decay rate holds in the $L^1\t…
Smoothing and Global Attractors for the Zakharov System on the Torus
Burak Erdogan, Nikolaos Tzirakis
In this paper we consider the Zakharov system with periodic boundary conditions in dimension one. In the first part of the paper, it is shown that for fixed initial data in a Sobol…
Long time dynamics for forced and weakly damped KdV on the torus
Burak Erdogan, Nikolaos Tzirakis
The forced and weakly damped Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. Starting from and mean-zero initial data we prove that the solu…
Global Smoothing for the Periodic KdV Evolution
Burak Erdogan, Nikolaos Tzirakis
The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for initial data, , and for any , the diffe…
Strichartz and Smoothing Estimates for Schroedinger Operators with Large Magnetic Potentials in R^3
M. Burak Erdogan, Michael Goldberg, Wilhelm Schlag
We show that the time evolution of the operator in R^3 satisfies Strichartz and smoothing estimates under suitable smoothness and d…