University of California, Irvine

Department of Mathematics

                        Professor Edriss S. Titi
                 Mathematics, Mechanical and Aerospace Engineering

Rowland Hall Building

Room 510C
Irvine, CA 92697-3875 
(949) 824-3156 
(949) 824-7993 Fax 
etiti@math.uci.edu

   OFFICE HOURS: Mondays 12:00noon-1:00PM

                                Wednesdays 10:00AM-11:00AM

 

TEACHING

 

Math-2B

 

First Midterm on Friday, October 23, 2009.

Course Policy

Suggested Syllabus

Homework

Webwork

 

 

PUBLICATIONS

 

(Please contact me at etiti@math.uci.edu for preprints and reprints)
 

RECENT PREPRINTS

A.V. Babin, A.A. Ilyin, and E.S. Titi, On the regularization mechanism for the spatially periodic Korteweg-de Vries equation, (submitted).

 

A. Larios and E.S. Titi, On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models, Discrete and Continuous Dynamical Systems, (submitted).  (An invite article for a special issue in honor of Professor P. Kloeden on the occasion of his 60th  birthday).

 

F. Ramos and E.S. Titi, Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit, Discrete and Continuous Dynamical Systems, (submitted). (An invite article for a special issue in honor of Professor R. Temam on the occasion of his 70th birthday).

 

Z. Artstein, C.W. Gear, I.G. Kevrekidis, M. Slemrod and E.S. Titi, Analysis and Computation of a discrete KdV-Burgers type equation with fast dispersion and slow diffusion, (submitted).

 

Q. Jiu, D. Niu, E.S. Titi and Z. Xin, Axisymmetric Euler-α equations without swirl: existence, uniqueness and Radon measure valued solutions, (submitted).


C. Cao, S. Chen and E.S. Titi, A turbulence model for the 1D dispersive wave, (submitted). (pdf) ( ps )

 

PAPERS TO APPEAR

C. Bardos and E.S. Titi, Loss of smoothness and energy conserving rough weak solutions for the 3d Euler equations, Discrete and Continuous Dynamical Systems, (to appear). (An invite article for a special issue in honor of Professor V. Solonnikov on the occasion of his 75th birthday).

 

C. Bardos, J. Linshiz and E.S. Titi, Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the 2D Euler equations, Communications in Pure and Applied Mathematics, (in press).

 

V.K. Kalantarov and E.S. Titi, Global attractors and determining modes for the 3D Navier-Stokes-Voight equations, Chinese Annals of Mathematics, (in press). (pdf) (An invited article for a special issue in honor of Professor A. Majda on the occasion of his 60th birthday).

 

B. Levant, F. Ramos and E.S. Titi, On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model, Communications in Mathematical Sciences, (2009), (in press).  (An invite article for a special issue in honor of Professor A. Majda in the occasion of his 60th birthday).

 

Y. Cao and E.S. Titi, On the rate of convergence of the two-dimensional α-models Of turbulence to the Navier-Stokes equations, Numerical Functional Analysis and Optimization, (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

120. C. Bardos, U. Frisch, W. Pauls, S.S. Ray, and E.S. Titi, Entire solutions of hydrodynamical equations with exponential dissipation, Communications in Mathematical Physics, 293 (2010), 519–543.

 

118. A.-C. Bennis, R. Lewandowski and E.S. Titi, Simulations de l'écoulement turbulent marin ave un modéle de déeconvolution, Comptes Rendus De L'Académie Des Sciences, Paris,  Série I ,  347 (2009), 445-450.

 

117. Y. Cao, Z.H. Musslimani and E.S. Titi, Modulation theory for self-focusing in the nonlinear Schrödinger-Helmholtz equation, Numerical Functional Analysis and Optimization, 30 (2009), 46-69.

 

116. 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, SIAM, Journal on Mathematical Analysis, 41(1) (2009), 269–296.

 

115. V.K. Kalantarov, B. Levant and E.S. Titi, Gevrey regularity of the global attractor of the 3D Navier-Stokes-Voight equations, Journal of Nonlinear Science, 19 (2009), 133-152.

 

114. C. Cao and E.S. Titi, Regularity criteria for the three-dimensional Navier-Stokes equations, Indiana University Mathematics Journal, 57(6) (2008), 2643-2662 (2008). (An invite article for a special issue in honor of Professor C. Foias in the occasion of his 75th birthday).

 

113. E. Olson and E.S. Titi, Determining modes and Grashof number in 2D turbulence - A

numerical case study, Theoretical and Computational Fluid Dynamics, 22(5) (2008), 327-339.

 

112. B.J. Geurts, A. Kuczaj and E.S. Titi, Regularization modeling for large-eddy simulation of homogeneous isotropic decaying turbulence, Journal of Physics A, 41 (2008), 344008 (29pp). (An invite article for a special issue in honor of Professor D.D. Holm in the occasion of his 60th birthday).

 

111. Y. Cao, Z.H. Musslimani and E.S. Titi, Nonlinear Schrödinger-Helmholtz equation as numerical regularization of the nonlinear Schrödinger equation, Nonlinearity, 21 (2008), 879-898. (pdf)

 

110. E. Lunasin, S. Kurien and E.S. Titi, Spectral scaling of α-models for two-dimensional turbulence, Journal of Physics A, 41 (2008), 344014 (10pp). (An invite article for a special issue in honor of Professor D.D. Holm in the occasion of his 60th birthday).

109. 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, 245 (2008), 2771-2784.

108. 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, 237, (2008) 1905-1911. An invited article for a special issue in the occasion of 250 years for the Euler Equations.

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)

100. B. Khouider and E.S. Titi, An inviscid regularization for the surface quasi-geostrophic equation, Communications in Pure and Applied Mathematics, 61(10) (2008), 1331-1346. (pdf)

 

99. C. Cao , J. Qin and E.S. Titi, Regularity criterion for solutions of three-dimensional turbulent channel flows, Communications in Partial Differential Equations,   33(1-3) (2008), 419-428. (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, I. G. Kevrekidis and E. S. Titi , Asymptotic States of a Smoluchowski Equation , Archive of Rational Mechanics and Analysis,  174(3) (2004), 365-384. ( pdf ) (ps)

 

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, S. Benachour and E.S. Titi, Finite-time singularity versus global regularity for hyperviscous Hamilton-Jabcobi-like equations, Nonlinearity, 16 (2003), 1967-1989. (pdf ) ( ps )

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, SIAM, Journal of Numerical Analysis, 37 (2000), 470-499.

 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)