Nikolaos Tzirakis

Research

My research area is Harmonic Analysis and Partial Differential Equations (PDE). More precisely I am interested in the long time behavior of the Cauchy problem for dispersive nonlinear PDE . Most of my work is concentrated on the study of the semilinear Schrodinger equation (focusing or defocusing).

Professional Information

2004, Ph.D. in Mathematics, University of Massachusetts at Amherst.
2004-2005, Institute for Advanced Study at Princeton, Member.
2005-2007, University of Toronto, Postdoctoral Fellow.
2007-\ \ \ \ , University of Illinois at Urbana-Champaign, Assistant Professor.

Recent Publications and Preprints

• (with Justin Holmer)Asymptotically linear solutions in $H^1$ of the 2-d defocusing nonlinear Schroedinger and Hartree equations, submitted pdf file.
• (with J. Colliander and M. Grillakis) Tensor products and correlation estimates with applications to nonlinear Schroedinger equations, submitted. pdf file.
• (with J. Colliander and M. Grillakis) Improved interaction Morawetz inequalities for the cubic nonlinear Schroedinger equation in 2d. To appear in International Mathematics Research Notices, pdf file.
• (with D. De Silva, N. Pavlovic and G.Staffilani) Global well-posedness and polynomial bounds for the defocusing nonlinear Schroedinger equation in 1d. To appear in Communications in Partial Differential Equations, pdf file.
• (with D. De Silva, N. Pavlovic and G.Staffilani) Global Well-Posedness for the L^2-critical nonlinear Schroedinger equation in higher dimensions. To appear in Communications on Pure and Applied Analysis, pdf file.
• (with D. De Silva, N. Pavlovic and G.Staffilani) Global well-posedness for a periodic nonlinear Schroedinger equation in 1d and 2d. To appear in Discrete and Continuous Dynamical Systems, pdf file.
• (with J. Colliander and J. Holmer) Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schroedinger systems. To appear in Trans. Amer. Math. Soc., pdf file.
• Mass concentration phenomenon for the quintic nonlinear Schroedinger equation in one dimension. SIAM J. Math. Anal. 37 (2006), no. 6, 1923--1946, pdf file.
• (with P. G. Kevrekidis)On the collapse arresting effects of discreteness. Math. Comput. Simulation 69 (2005), no. 5-6, 553--566.
• The Cauchy problem for the Klein-Gordon-Schroedinger system in low dimensions below the energy space. Comm. Partial Differential Equations 30 (2005), no. 4-6, 605--641.
• The Cauchy problem for the semilinear quintic Schroedinger equation in one dimension. Differential Integral Equations 18 (2005), no. 8, 947--960.
• (with Arpad Benyi) Multilinear almost diagonal estimates and applications. Studia Math. 164 (2004), no. 1, 75--89.

Teaching