Nonlinear Partial Differential Equations, Turbulence Theory, Navier-Stokes Equations, Computational Mathematics
Award of Outstanding Contributions to Undergraduate Education, School of Physical Sciences, UCI, (1991-1992),(2002-2003).
Orson Anderson Visiting Scholar, Los Alamos National Laboratory (1997-1998).
Varon Visiting Professorship, Weizmann Institute of Sciences, Israel (1999).
Stanislaw M. Ulam Visiting Scholar, Los Alamos National Laboratory (2002-2003).
Fellow of the Institute of Physics, UK, (2004-present).
Member of the Editorial Board "International Journal of Differential Equations and Applications" (1999-present).
Member of Editorial Board: "Numerical Functional Analysis and Optimization" (2002-Present).
Member of the Editorial Board "Nonlinearity" (2002-Present).
1986-1988: L.E. Dickson Instructor, Department of Mathematics, The University of Chicago.
I am interested in the long-time behavior of solutions to dissipative Partial Differential Equations, such as the Navier-Stokes equations, and in designing numerical method for integrating them. Also, I am interested in identifying the degrees of freedom that mentor this finite dimensional long-time behavior in order to be able to control these solutions.
C.R. Doering and E.S. Titi, Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations, Physics of Fluids, Vol. 7, No. 6 (1995), pp. 1384-1390.
S. Chen, C. Foias, D. Holm, E. Olson, E.S. Titi, and S. Wynne, The Camassa--Holm equations and turbulence, Physica D, Vol. 133,(1999), 49-65.
C. Foias, D. Holm and E.S. Titi,
The three dimensional viscous Camassa-Holm equations and their relation to the Navier--Stokes equations and turbulence theory, Journal of Dynamics and Differential Equations, Vol. 14 (2002), 1-35.
C. Cao, I. Kevrekidis and E.S. Titi, Numerical criterion for the stabilization of steady states of the Navier-Stokes equations, Indiana University Mathematics Journal, Vol. 50 (2001), 37-96.(Special Issue in Honor of C. Foias and R. Temam).
C. Cao and E.S. Titi, Global well-posedness and finite dimensional
global attractor for a 3-D planetary geostrophic viscous model,
Communications in Pure and Applied Mathematics, Vol. 56 (2003),198-233.
M. Oliver and E.S. Titi, Gevrey regularity for the attractor of a
partially dissipative model of Benard convection in a porous medium, Journal of Differential Equations, Vol. 163 (2000), 292-311.
H. Bellout, S. Benachour and E.S. Titi, Finite-time singularity versus global regularity for hyperviscous Hamilton-Jabcobi-like equations, Nonlinearity, 16 (2003), 1967-1989.
C. Foias, D. Holm and E.S. Titi, The Navier--Stokes-alpha model of fluid turbulence, Physica D, Vol. 152 (2001), 505-519.(Special
Issue in Honor of V.E. Zakharov on the Occasion of His 60th Birthday).
Y. Chung and E. S. Titi, Inertial manifolds and Gevrey regularity for
the Moore--Greitzer model of an axial--flow compressor, Journal
Nonlinear Science, Vol. 13 (2003), 1-26.
L. Margolin, E.S. Titi and S. Wynne, The postprocessing Galerkin and nonlinear Galerkin methods - a truncation analysis point of view, SIAM Journal of Numerical Analysis, Vol. 41 (2003), 695-714.
P. Constantin, E. S. Titi and J. Vukadinovic,Dissipativity and Gevrey regularity of a Smoluchowski equation, Indiana University Mathematics Journal, Vol. 54 (4)(2005), 949-970.
E. Olson And E.S. Titi, Determining modes for continuous data assimilation in 2-D turbulence, Journal of Statistical Physics, Vol. 113 (2003), 799-840.
P. Constantin, I. Kevrekidis and E.S. Titi, Remarks on a Smoluchowski equation, Discrete and Continuous Dynamical Systems, Vol. 11 (2004), 101-112.
P. Constantin, I. G. Kevrekidis and E. S. Titi, Asymptotic states of a Smoluchowski equation, Archive of Rational Mechanics and Analysis, Vol. 174 (2004), 365-384.
A. Cheskidov, D. D. Holm, E. Olson, and E. S. Titi, On a Leray-alpha Model of Turbulence, Royal Society London, Proceedings, Series A, Mathematical, Physical Engineering Sciences, Vol. 461(2005), 629-649.
A. Ilyin, A. Miranville and E. S. Titi, Small viscosity sharp estimates for the global attractor of the 2-D damped-driven Navier--Stokes equations, Communications in Mathematical Sciences, Vol. 2 (2004), 403-426.
C. Cao, E.S. Titi and M. Ziane, A "horizontal" hyper--diffusion 3-D thermocline planetary geostrophic model: well-posedness and long time behavior, Nonlinearity, Vol. 17 (2004), 1749-1776.
AMS, SIAM, IMU
Weizmann Institute of Science, since 2003