We review the properties of the nonlinearly dispersive Navier–Stokes-alpha (NS-α) model of
incompressible fluid turbulence—also called the viscous Camassa–Holm equations in the …

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 …

We propose a new class of models for the mean motion of ideal incompressible fluids in
three dimensions, including stratification and rotation. In these models, the amplitude of the …

We explore the utility of the recently proposed alpha equations in providing a subgrid model
for fluid turbulence. Our principal results are comparisons of direct numerical simulations of …

The energy-equation approach used to prove the existence of the global attractor by
establishing the so-called asymptotic compactness property of the semigroup is considered …

In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a
second grade fluid in a plane channel with impermeable solid walls, taking into account the …

This paper deals with an initial-boundary value problem modeling the unidirectional
pressure-driven flow of a second grade fluid in a plane channel with impermeable solid …

Many real fluids exhibit response characteristics that cannot be satisfactorily described by
the classical Navier–Stokes fluid model and such fluids are referred to as non-Newtonian …

This paper treats the solvability of the equations of motion for an incompressible fluid of
grade two subject to nonlinear partial slip boundary conditions in a bounded simply …

This paper develops the geometric analysis of geodesic ow of a new right invariant metric
⟨⋅,⋅\rangle_1 on two subgroups of the volume preserving diffeomorphism group of a …