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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
Onsager's conjecture on the energy conservation for solutions of Euler's equation
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
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
Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models
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
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
Continuous Data Assimilation Using General Interpolant Observables
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
Global attractors and determining modes for the 3D Navier-Stokes-Voight equations
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
Analytical study of certain magnetohydrodynamic-α models
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
On a Leray–α model of turbulence
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
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