We review the properties of the nonlinearly dispersive Navierâ€“Stokes-alpha (NS-Î±) model of incompressible fluid turbulence â€” also called the viscous Camassaâ€“Holm equations in the literature. We firstâ€¦ (More)

1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 2Department of Mathematics, Indiana University, Bloomington, Indiana 47405 3Departmentâ€¦ (More)

In this paper, we study the long-time behavior of a class of nonlinear dissipative partial differential equations. By means of the Lyapunov-Perron method, we show that the equation has an inertialâ€¦ (More)

In this paper we discuss recent progress in using the Camassaâ€“Holm equations to model turbulent flows. The Camassaâ€“Holm equations, given their special geometric and physical properties, appearâ€¦ (More)

In this note we discuss the HÂ¿-sensitivity minimitization problem for linear time-invariant delay systems. While the unweighted case reduces to simple Nevanlinna-Pick interpolation, the weighted caseâ€¦ (More)

We consider the Navier-Stokes equations of a viscous incompressible fluid, and we want to see to what extent these solutions can be determined by a discrete set of nodal values of these solutions.â€¦ (More)

for X in &(Â£?). This paper was motivated by the question: to what extent does C(TfS) behave like a normal operator on Hubert space? It will be shown that C(T, S) does share many of the specialâ€¦ (More)

Let C denote the category of Hilbert modules which are similar to contractive Hilbert modules. It is proved that if H0, H âˆˆ C and if H1 is similar to an isometric Hilbert module, then the sequence 0â†’â€¦ (More)

The determining modes for the two-dimensional incompressible Navier-Stokes equations (NSE) are shown to satisfy an ordinary differential equation of the form dv/dt = F (v), in the Banach space, X, ofâ€¦ (More)