The projects that I plan to expand on over the next few years concern the mathematical analysis of certain turbulence models and related equations. My research also involves the direct numerical simulation of these equations with applications to optimal stirring strategies for passive scalars and mixing, data assimilation, which is of practical interest to weather and climate prediction, image reconstruction, and nonlinear control theory with vast engineering applications.

Publications
As of 2018, here are the papers I have published:
 A. Farhat, E. Lunasin and E. S. Titi, A Data Assimilation Algorithm: The Paradigm of the 3D Leray$\alpha$ Model of Turbulence, Nonlinear Partial Differential Equations Arising from Geometry and Physics, Cambridge University Press, London Mathematical Society, Lecture Notes Series.
 E. Lunasin and E.S. Titi, Finite determining parameters feedback control for distributed nonlinear dissipative systems  a computational study, Evolution Equations and Control Theory, 6, no. 4 (2017), 535557.
 A. Farhat, E. Lunasin and E. S. Titi, On the Charney conjecture of data assimilation employing temperature measurements alone: The paradigm of 3D Planetary Geostrophic model, Mathematics of Climate and Weather Forecasting, 2, (2016), 6174.
 A. Farhat, E. Lunasin and E. S. Titi, Continuous data assimilation for a 2D Benard convection system through horizontal velocity measurements alone, J. Nonlinear Science, 2, (2016), 10651087.
 A. Farhat, E. Lunasin and E. S. Titi, Data assimilation algorithm for 3D Benard convection in porous media employing only temperature measurements, Journal of Math. Anal. and App. 438 (1), (2016), 492  506.
 E. Lunasin, R. MalekMadani and M. Slemrod, A dynamical systems approach to mathematical modeling of tornadoes, Bull. Inst. Math. Acad. Sinica 11 (1), (2016), 141161.
 A. Farhat, E. Lunasin and E.S. Titi, Abridged continuous data assimilation for the 2D NavierStokes equations utilizing measurements of only one component of the velocity field, Journal of Mathematical Fluid Mechanics 18 (1), (2016), 123.
 A. Farhat, M.S. Jolly and E. Lunasin, Bounds on energy and enstrophy for the 3D NavierStokes$\alpha$ and Leray$\alpha$ models, Communications on Pure and Applied Analysis 13, (2014) 21272140.
 A. Larios, E. Lunasin and E.S. Titi, Global wellposedness for the 2D Boussinesq system without heat diffusion and with anisotropic viscosity, J. Differential Equations 255, (2013), 26362654.
 E. Lunasin, Z. Lin, A. Novikov, A. Mazzucato and C. Doering, Optimal Stirring Strategies with finite energy, finite power or finite palenstrophy constraint, Journal of Mathematical Physics 53, (2012), 115.
 M. Ebrahimi, M. Holst and E. Lunasin, The NavierStokes Voight for image inpainting, IMA Journal of Applied Mathematics (2012), 126.
 B. Wen, N. Dianati, E. Lunasin, G. Chini and C. Doering, New upper bounds and reduced dynamical modeling for RayleighBenard convection in a fluid saturated porous layer, Comm. Nonlinear Science and Num. Simulations, 17 (5), (2011), 21912199.
 M. Holst, E. Lunasin and G. Tsotgtgerel, Analytical study of generalized $\alpha$models of turbulence, Journal of Nonlinear Science, 20 (5), (2010), 523567.
 E. Lunasin, S. Kurien and E.S. Titi, Spectral scaling of the Leray$\alpha$ model for twodimensional turbulence, Journal of Physics A: Math. Theor. 41, (2008), 344014.
 E. Lunasin, S. Kurien, M. Taylor and E.S. Titi, A study of the NavierStokes$\alpha$ model for twodimensional turbulence,Journal of Turbulence, 8, (2007), 751778.
 Y. Cao, E. Lunasin, and E.S. Titi, Global wellposedness of viscous and inviscid simplified Bardina turbulence models, Communications in Mathematical Sciences 4, no. 4, (2006), 823847.
 A. Ilyin, E. Lunasin and E.S. Titi, A modifiedLeray$\alpha$ subgrid scale model of turbulence, Nonlinearity 19, (2006), 879897.
Ph.D. Thesis: Analytical and numerical study of certain subgrid scale $\alpha$models of turbulence. University of California, Irvine, (2007).

Collaborators
My background in scientific computing and the mathematical theory of fluid dynamics has opened many doors to collaborate with researchers in numerous institutes. Here is an incomplete list of current and past collaborators.
 Svetlana AvramovZamurovic, United States Naval Academy
 Cody Brownel, United States Naval Academy
 Charles Doering, University of Michigan
 Aseel Farhat, Florida State University
 Michael Holst, University of California, San Diego
 Athanasios Iliopoulos, U.S. Naval Research Laboratory
 Alexei Ilyin, Keldysh Institute of Applied Mathematics
 Michael Jolly, Indiana University
 Susan Kurien, Los Alamos National Laboratory
 Adam Larios, University of Nebraska, Lincoln
 Reza MalekMadani, United States Naval Academy
 Anna Mazzucato, Penn State University
 John Michopoulos, U.S. Naval Research Laboratory
 Charles Nelson, United States Naval Academy
 Brice Nguelifack, United States Naval Academy
 Alexei Novikov, Penn State University
 Mark Petersen, Los Alamos National Laboratory
 Marshall Slemrod, Weismann Institute of Science
 Mark A. Taylor, Sandia National Laboratory
 Edriss S. Titi, Texas A&M University, Weismann Institute of Science
 Gantumur Tsogtsegerel, McGill University