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), 535--557.
- 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), 61--74.
- 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), 1065--1087.
- 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. Malek-Madani and M. Slemrod, A dynamical systems approach to mathematical modeling of tornadoes, Bull. Inst. Math. Acad. Sinica 11 (1), (2016), 141--161.
- A. Farhat, E. Lunasin and E.S. Titi, Abridged continuous data assimilation for the 2D Navier-Stokes equations utilizing measurements of only one component of the velocity field, Journal of Mathematical Fluid Mechanics 18 (1), (2016), 1--23.
- A. Farhat, M.S. Jolly and E. Lunasin, Bounds on energy and enstrophy for the 3D Navier-Stokes-$\alpha$ and Leray-$\alpha$ models, Communications on Pure and Applied Analysis 13, (2014) 2127--2140.
- A. Larios, E. Lunasin and E.S. Titi, Global well-posedness for the 2D Boussinesq system without heat diffusion and with anisotropic viscosity, J. Differential Equations 255, (2013), 2636--2654.
- 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), 1--15.
- M. Ebrahimi, M. Holst and E. Lunasin, The Navier-Stokes Voight for image inpainting, IMA Journal of Applied Mathematics (2012), 1--26.
- B. Wen, N. Dianati, E. Lunasin, G. Chini and C. Doering, New upper bounds and reduced dynamical modeling for Rayleigh-Benard convection in a fluid saturated porous layer, Comm. Nonlinear Science and Num. Simulations, 17 (5), (2011), 2191--2199.
- M. Holst, E. Lunasin and G. Tsotgtgerel, Analytical study of generalized $\alpha$-models of turbulence, Journal of Nonlinear Science, 20 (5), (2010), 523--567.
- E. Lunasin, S. Kurien and E.S. Titi, Spectral scaling of the Leray-$\alpha$ model for two-dimensional turbulence, Journal of Physics A: Math. Theor. 41, (2008), 344014.
- E. Lunasin, S. Kurien, M. Taylor and E.S. Titi, A study of the Navier-Stokes-$\alpha$ model for two-dimensional turbulence,Journal of Turbulence, 8, (2007), 751--778.
- Y. Cao, E. Lunasin, and E.S. Titi, Global well-posedness of viscous and inviscid simplified Bardina turbulence models, Communications in Mathematical Sciences 4, no. 4, (2006), 823--847.
- A. Ilyin, E. Lunasin and E.S. Titi, A modified-Leray-$\alpha$ sub-grid scale model of turbulence, Nonlinearity 19, (2006), 879--897.
Ph.D. Thesis: Analytical and numerical study of certain sub-grid scale $\alpha-$models of turbulence. University of California, Irvine, (2007).