Explosive instabilities for a generalized second grade fluid

An analysis of the Rayleigh–Stokes problem for a generalized second-grade fluid

We study the Rayleigh-Stokes problem for a generalized second-grade fluid which involves a Riemann-Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data [Formula: see text], including [Formula: ...

Exact solutions for the flow of a generalized second grade due to a Longitudinal quadratic time-dependent shear stress

Unsteady Falkner-skan Flow of a Second Grade Fluid

The non-similar solutions for the unsteady flow of a second grade fluid wereconstructed. The method of perturbation was used for the solution of the governing non-linear equation. The results of Rajagopal et al. (Int. J. Non-Linear Mechanics, 1983) can be obtained as a special case of the presented analysis.

exact solutions for the flow of a generalized second grade due to a longitudinal quadratic time-dependent shear stress

Theory for explosive ideal magnetohydrodynamic instabilities in plasmas.

Flux tubes confined in tokamaks are observed to erupt explosively in some plasma disruptions and edge localized modes. Similar eruptions occur in astrophysical plasmas, for example, in solar flares and magnetospheric substorms. A single unifying nonlinear evolution equation describing such behavior in both astrophysical and tokamak plasmas is derived. This theory predicts that flux tubes rise e...