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Department of Mathematics |
Professor Edriss S. Titi
Mathematics, Mechanical and Aerospace Engineering
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Multipurpose Science & Technology Building
OFFICE HOURS: By Appointment |
TEACHING
PUBLICATIONS
RECENT PREPRINTS
Y. Cao, Z.H. Musslimani and E.S. Titi, Nonlinear Schrödinger-Helmholtz equation as numerical regularization of the
nonlinear Schrödinger equation, (submitted). (pdf)
B. Ettinger
and E.S. Titi, Global existence and uniqueness of weak solutions of 3-D
Euler equations with helical
symmetry in the absence of vorticity stretching, (submitted).
B.J. Geurts,
A. Kuczaj and E.S. Titi, Regularization modeling
for large-eddy simulation of
homogeneous isotropic decaying turbulence, (submitted).
V.K. Kalantarov,
B. Levant and E.S. Titi, Gevrey regularity
of the global attractor of the 3D
Navier-Stokes-Voight equations, (submitted).
E. Lunasin,
S. Kurien and E.S. Titi, Spectral scaling of α-models
for two-dimensional
turbulence, (submitted).
E. Olson and E.S. Titi,
Determining modes and Grashof number in 2D
turbulence—A
numerical case study, (submitted).
V.K. Kalantarov
and E.S. Titi, Global attractors and determining modes for the 3D
Navier-Stokes-Voight equations,
(submitted). (pdf)
C. Cao, S. Chen and E.S. Titi, A turbulence model
for the 1D dispersive wave, (submitted). (pdf) ( ps )
PAPERS TO APPEAR
B. Khouider
and E.S. Titi, An inviscid regularization for the
surface quasi-geostrophic equation,
Communications in Pure and Applied Mathematics, (to appear). (pdf)
C. Cao
and E.S. Titi, Regularity criterion for solutions of three-dimensional
turbulent channel flows, Communications in Partial Differential Equations,
(submitted). (pdf)
C. Bardos, J. Linshiz and E.S. Titi, Global regularity for a Birkhoff-Rott-α approximation of the dynamics of
vortex sheets of the 2D Euler equations, Invited article in the occasion of
250 years for the Euler Equations, Physica D, (to
appear).
G. Katriel, R. Kupferman and E.S. Titi, Long-time limit for a class of quadratic infinite-dimensional
dynamical systems inspired by models of viscoelastic
fluids, Journal of Differential Equations, (to appear).
SELECTED RECENTLY PUBLISHED PROCEEDINGS PAPERS
6. K.Ríos-Soto, C.
Castillo-Chavez, M. Neubert, E.S. Titi, A. Yakubu, Epidemic spread in population demographic
equilibrium, Proceeding of the Snowbird Conference on Modeling The Dynamics
of Human Diseases: Emerging Paradigms and Challenges. Eds. A. Gumel (Chief Editor), C. Castillo-Chavez, D.P. Clemence, and R.E. Mickens, (2006).
5. C. Cao and E. S. Titi, Asymptotic behavior of
viscous 1--D scalar conservation laws with Neumann boundary conditions,
Third Palestinian Mathematics Conference, Bethlehem University, West Bank,
Mathematics & Mathematics Education,
S. Elaydi, E. S.
Titi, M. Saleh, S. K. Jain
and R. Abu Saris, editors, World Scientifc,
2002. (
pdf ) ( ps )
SELECTED RECENTLY PUBLISHED JOURNAL PAPERS
107. Z. Artstein, J. Linshiz and E.S. Titi, Young measure approach to
computing slowly advancing fast oscillations, SIAM, Multiscale
Modeling and Simulation, 6(4) (2007),
1085-1097.
106. R. Kupferman, C. Mangoubi and E.S. Titi, A Beale-Kato-Majda
breakdown criterion for an Oldroyd-B fluid in the
creeping flow regime, Communications in Mathematical Sciences, 6(1) (2008).
105. Z. Artstein, I.G.
Kevrekidis, M. Slemrod and
E.S. Titi, Slow observables of singularly perturbed differential equations,
Nonlinearity, 20 (2007), 2463-2481.
104.
V.V. Chepyzhov, E.S. Titi, and M.I. Vishik, On convergence of trajectory attractors of 3D Navier--Stokes-α model as α approaches 0, Matematicheskii Sbornik, 198:12 (2007), 3-36. (pdf-English) (pdf-Russian).
103. C. Bardos
and E.S. Titi, Euler equations of incompressible ideal fluids, Uspekhi Matematicheskikh Nauk, UMN 62:3(375) (2007), 5–46. Also in Russian Mathematical Surveys, 62(3) (2007),
409-451.
102. E.M. Lunasin,
S. Kurien, M. Taylor and E.S. Titi, A study of the
Navier-Stokes-α model for two-dimensional
turbulence, Journal of Turbulence, 8(1) (2007), 1-21. (pdf)
101. R. Benzi,
B. Levant, I. Procaccia and E.S. Titi, Statistical
properties of nonlinear shell models of turbulence from linear advection
models: rigorous results, Nonlinearity, 20(6) (2007), 1431-1443. (pdf)
98. P. Constantin, B.
Levant and E.S. Titi, Sharp lower bounds for the dimension of the global
attractor of the Sabra shell model of turbulence,
Journal of Statistical Physics, 127(6) (2007), 1173-1192. (pdf)
97.
A.A. Ilyin and E.S. Titi, On the domain of
analyticity and small scales for the solutions of the damped-driven 2D Navier-Stokes equations, Dynamics of Partial
Differential Equations, 4(2) (2007), 111-127. (pdf)
96. P. Constantin, B.
Levant and E.S. Titi, A note on the regularity of inviscid
shell model of turbulence, Physics Review E, 75 (2007), 016304.(pdf)
95. Y. Cao, E.M. Lunasin and E.S. Titi, Global well-posedness
of three-dimensional viscous and inviscid simplified Bardina turbulence models, Communications in
Mathematical Sciences, 4(4) (2006), 823-84. (pdf)
94. P. Constantin, C. Fefferman, E.S. Titi and
A. Zarnescu, Regularity of coupled
two-dimensional Nonlinear Fokker-Planck and Navier-Stokes
Systems, Communications in Mathematical Physics, 270(3) (2007), 789-812. (pdf)
93. J. Linshiz
and E.S. Titi, Analytical study of certain magnetohydrodynamics-α
models, Journal of Mathematical Physics, 48 (2007), 065504.
92. S.I. Chernyshenko,
P. Constantin, J.C. Robinson and E.S. Titi,
A posteriori regularity of the three-dimensional Navier-Stokes
equations from numerical computations, Journal of Mathematical Physics, 48
(2007), 065204.
91. Y. Cao and E.S.
Titi, Trivial stationary solutions to the Kuramoto-Sivashinsky
and certain nonlinear elliptic equations, Journal of Differential
Equations, 231 (2006), 755-767. (pdf)
90. A.A. Ilyin and
E.S. Titi, The
damped-driven 2D Navier-Stokes system on large
elongated domains, Journal of Mathematical
Fluid Mechanics, DOI10.1007/s00021-006-0226-6, (2007).
89. V.V. Chepyzhov,
E.S. Titi, and M.I. Vishik, On the convergence of solutions of the Leray-α model to the trajectory attractor of the 3D Navier--Stokes system, Journal of Discrete and
Continuous Dynamical Systems - Serie A, 17(3)
(2007), 33-52.
88. P. Constantin, B.
Levant, E.S. Titi, Analytic study of
shell models of turbulence, Physica D, 219(2) (2006), 120-141.
87. E. Olson and E.S. Titi, Viscosity versus vorticity stretching: global well-posedness
for a family of the Navier-Stokes alpha-like models,
Nonlinear Analysis Series A: Theory Methods, 66(11) (2007), 2427-2458.
86. A.A. Ilyin, E.M. Lunasin and E.S.
Titi, A modified-Leray-α sub-grid scale model
of turbulence, Nonlinearity, 19 (2006), 879-897. (pdf)
85. C. Cao and
E.S. Titi, Global well-posedness of the
three-dimensional viscous primitive equations of large scale ocean and
atmosphere dynamics, Annals of Mathematics, 166(1)
(2007), 245-267.
84. A.A. Ilyin and
E.S. Titi, Sharp estimates for the number of
degrees of freedom for the damped-driven 2D Navier-Stokes
equations, Journal of Nonlinear Science, 16(3) (2006), 233-253.
83. D. Holm and E.S. Titi, Computational
models of Turbulence: The LANS-α model and the role of global analysis,
Feature Article: SIAM News, 38(7), September 2005.
82. J.D. Gibbon and E.S. Titi, Cluster formation in complex multi-scale systems, Royal Society London, Proceedings, Series A, Mathematical, Physical & Engineering Sciences, 461 (2005), 3089-3097. (pdf) (ps)
80. P. Constantin, E.
S. Titi and J. Vukadinovic, Dissipativity
and Gevrey regularity of a Smoluchowski equation, Indiana University Mathematics
Journal, 54 (4) (2005), 949-970. (pdf )(ps )
79. 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, 2(3) (2004), 403-426.( pdf)( ps )
78. A. Cheskidov,
D. D. Holm, E. Olson and E. S. Titi, On a Leray-α
Model of Turbulence, Royal Society London, Proceedings, Series
A, Mathematical, Physical & Engineering Sciences, 461
(2005), 629--649. ( pdf )
( ps )
77. 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, 17
(2004), 1749-1776. (
pdf )(
ps ).
76. M. I. Vishik, E. S.
Titi and V.V.Chepyzhov, Trajectory attractor
approximations of the 3D Navier—Stokes system
by a Leray-α model, Russian Mathematical Dokladi (Translated from Russian), 71 (2005), 92-95. (English-
pdf )(English-ps )(Russian-pdf )(Russian-ps )
75. P. Constantin,
74. C. Cao, D. Holm and E.S. Titi, Traveling wave solutions for a class of one-dimensional nonlinear shallow water wave models, Journal of Dynamics and Differential Equations, 16(1) (2004), 167-178, (pdf) (ps).
73. A.A. Ilyin and
E.S. Titi, Attractors to the two-dimensional Navier-Stokes-α
model: An alpha-dependence study, Journal of Dynamics and Differential
Equations, 15 (2003), 751-777. (
pdf ) (
ps)
72. H. Bellout,
71. P. Constantin, I. Kevrekidis and E.S. Titi, Remarks on a Smoluchowski equation, Discrete and Continuous Dynamical Systems, 11 (2004), 101-112. ( pdf) ( ps )
70. E. Olson and E.S. Titi, Determining modes for continuous data assimilation in 2-D turbulence, Journal of Statistical Physics, 113 (2003), 799-840. (pdf) ( ps )
69. 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, 41 (2003), 695-714.( pdf ) ( ps )
68. Y. Chung and E. S. Titi, Inertial manifolds and Gevrey regularity for the Moore-Greitzer model of turbo-machine engine, Journal of Nonlinear Science, 13 (2003), 1-26. (pdf ) ( ps )
67. C. Cao and E. S. Titi, Global well-posedness and finite dimesional global attractor for a 3-D planetary geostrophic viscous model, Communications in Pure and Applied Mathematics, 56 (2003), 198-233. ( pdf ) ( ps )
66. P.G. Kevrekidis, I. G. Kevrekidis, A. R. Bishop and E. S. Titi, A continum approach to discreteness, Physical Review E, 65 (2002), no. 4, 046613. ( pdf ) (ps ).
65. 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, (Special Issue in Honor of C. Foias and R. Temam), 50 (2001), 37-96. (pdf ) (ps )
64. 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, 14 (2002), 1-35. ( pdf ) ( ps )
63. C. Foias, I. Kukavica, M. Jolly and E.S. Titi, The Lorenz equations as a metaphore for the Navier—Stokes equations, Discrete and Continuous Dynamical Systems, 7 (2001), 403-429.
62. C. Foias, D. Holm and E.S. Titi, The Navier--Stokes-alpha model of fluid turbulence, Physica D, (Special Issue in Honor of V. E. Zakharov on the Occasion of His 60th Birthday), D152 (2001), 505-519. ( pdf )(ps )
61. M. Oliver and E.S. Titi, On the domain of spatial analyticity for solutions of second order nonlinear analytic parabolic and elliptic differential equations , Journal of Differential Equations, 174 (2001), 55-74.
60. J. Novo, E.S.Titi and S. Wynne, Efficient methods using high accuracy approximate inertial manifolds, Numerische Mathematik, 87 (2001), 523-554.
59. B. Garcia--Archilla,
J. Novo and E.S. Titi, Postprocessing
Fourier spectral methods: the case of smooth solutions, Applied
Numerical Mathematics, 43 (2002), 191-209. (pdf) (ps
)
58. M. Oliver and E.S. Titi, Remark on the decay rate of higher order derivatives of solutions to the Navier--Stokes equations in Rⁿ, Journal of Functional Analysis, 172 (2000), 1-18. ( pdf ) ( ps )
57. M. Oliver and E.S. Titi, Gevrey regularity for the attractor of a partially dissipative model of Bénard convection in a porous medium, Journal of Differential Equations, 163 (2000), 292-311.
56. S. Chen, C. Foias, D. Holm, E. Olson, E.S. Titi, and S. Wynne, The Camassa--Holm equations and turbulence, Physica D, D133 (1999), 49-65. ( pdf )(ps ).
55. S. Shvartsman, C. Theodoropoulos, R. Rico-Martinez, I.G. Kevrekidis, E.S. Titi, and T. J. Mountziares, Order reduction of nonlinear dynamic models for distributed reacting systems, Journal of Process Control, 10 (2000), 177-184.
54. S. Chen, C. Foias, D. Holm, E. Olson, E.S. Titi and S. Wynne, A connection between Camass-Holm equations and turbulent flows in channels and pipes, Physics of Fluids, 11 (1999), 2343-2353.( pdf )(ps )
53. S. Chen, C. Foias, D. Holm, E. Olson, E.S. Titi and S. Wynne, The Camassa--Holm equations as a closure model for turbulent channel flow, Physical Review Letters, 81 (1998), 5338-5341. ( pdf ) ( ps )
52. B. Garcia-Archilla
and E.S. Titi, Postprocessing the Galerkin method: The finite elements case,
51. C. Cao, M. Rammaha and E.S. Titi, The Navier-Stokes equations on the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom, Zeitschrift fu"r Angewandte Mathematik und Physik (ZAMP), 50 (1999), 341-360.
50. H. Van Ly and E.S. Titi, Global Gevrey regularity for 3-D Bénard
convection in porous medium with zero Darcy-Prandtl number, Journal of Nonlinear Science, 9 (1999),
333-362.
43. A. Ferrari and E.S. Titi, Gevrey
regularity for nonlinear analytic parabolic equations, Communications
in Partial Differential Equations, 23 (1998), 1-16. (pdf) (ps)
26. D. Jones and E.S.
Titi, Upper bounds on the number of determining modes, nodes, and volume
elements for the Navier-Stokes equations,
Indiana University Mathematics Journal, 42 (1993), 875-887.
(Special Issue in Honor of Professor C. Foias on the
Occasion of his 60th Birthday). (pdf)
(ps)
2. E.S. Titi, On a criterion
for locating stable stationary solutions to the Navier-Stokes
equations, Nonlinear Analysis,
Theory, Methods and Applications, 11
(1987), 1085-1102. (pdf)