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Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics

In this paper we prove the global existence and uniqueness (regularity) of strong solutions to the three-dimensional viscous primitive equations, which model large scale ocean and atmosphere… Expand

Onsager's conjecture on the energy conservation for solutions of Euler's equation

- P. Constantin, E. Weinan, E. Titi
- Mathematics
- 1 October 1994

We give a simple proof of a result conjectured by Onsager [1] on energy conservation for weak solutions of Euler's equation.

The Three Dimensional Viscous Camassa–Holm Equations, and Their Relation to the Navier–Stokes Equations and Turbulence Theory

- C. Foias, Darryl D. Holm, E. Titi
- Mathematics
- 23 March 2001

We show here the global, in time, regularity of the three dimensional viscous Camassa–Holm (Navier–Stokes-alpha) (NS-α) equations. We also provide estimates, in terms of the physical parameters of… Expand

The Navier–Stokes-alpha model of fluid turbulence

- C. Foias, Darryl D. Holm, E. Titi
- Physics
- 23 March 2001

Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models

- Y. Cao, E. Lunasin, E. Titi
- Mathematics
- 9 August 2006

In this paper we present analytical studies of three-dimensional viscous and inviscid simplified Bardina turbulence models with periodic boundary conditions. The global existence and uniqueness of… Expand

On the regularization mechanism for the periodic Korteweg–de Vries equation

In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg–de Vries (KdV) equation in the homogeneous Sobolev spaces Ḣs for… Expand

Continuous Data Assimilation Using General Interpolant Observables

- A. Azouani, Eric Olson, E. Titi
- Mathematics, Computer ScienceJ. Nonlinear Sci.
- 3 April 2013

We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in… Expand

Global attractors and determining modes for the 3D Navier-Stokes-Voight equations

- V. Kalantarov, E. Titi
- Mathematics
- 27 May 2007

The authors investigate the long-term dynamics of the three-dimensional Navier-Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes… Expand

Analytical study of certain magnetohydrodynamic-α models

- Jasmine Linshiz, E. Titi
- Mathematics, Physics
- 23 June 2006

In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-α (also known as the… Expand

On a Leray–α model of turbulence

- A. Cheskidov, Darryl D. Holm, Eric Olson, E. Titi
- PhysicsProceedings of the Royal Society A: Mathematical…
- 8 March 2005

In this paper we introduce and study a new model for three–dimensional turbulence, the Leray–α model. This model is inspired by the Lagrangian averaged Navier–Stokes–α model of turbulence (also known… Expand

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