The effect of rotation on the Jeans instability of a self-gravitating viscoelastic fluid has been investigated using generalized hydrodynamic fluid equations. A dispersion relation is obtained using the linearized perturbation equations and normal mode analysis which is discussed for directions of rotation parallel and perpendicular to the wave propagation in classical (hydrodynamic) as well as kinetic limits. The Jeans criterion of instability is also obtained and it is found that it is unaffected by the presence of rotation in both the classical hydrodynamic and kinetic limits. The effects of Mach number, shear viscosity, sound velocity and rotation on the growth rate of the Jeans instability are also discussed numerically and we found that the shear viscosity and rotation have stabilizing influences on the growth rates of instability in both perpendicular and parallel propagations with finite angular rotation frequency. The stability of the rotating viscoelastic fluid is discussed using the Routh-Hurwitz criterion.

The Jeans instability of rotating viscoelastic fluid in the presence of uniform magnetic field is investigated using the generalised hydrodynamic (GH) model. A general dispersion relation is derived with the help of linearised perturbation equations using the normal mode analysis, which is further discussed for axis of rotation parallel and perpendicular to the direction of the magnetic field in both the weakly coupled (hydrodynamic) and strongly coupled (kinetic) limits. The onset criterion of Jeans instability for magnetised rotating viscoelastic fluid is obtained, which remains unaffected by the presence of rotation and magnetic field but depends upon viscoelastic effects. The graphical illustrations are depicted to see the influence of rotation, Mach number, shear and viscous effects, and sound speed on the growth rate of Jeans instability. It is found that all these parameters have stabilising influence on the growth rate of Jeans instability; hence, they are capable of collapsing to a self-gravitating, rotating, magnetised viscoelastic medium.

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Rayleigh-Taylor instability of stratified magnetized quantum plasma in a porous medium has been investigated. Medium is assumed to be highly conducting and incompressible. The relevant quantum magnetohydrodynamic equations are solved by using appropriate boundary conditions and a dispersion relation is obtained. The dispersion relation is derived for the case, where plasma is bounded by two rigid planes. The growth rate of unstable Rayleigh-Taylor mode and stability conditions of the medium are evaluated analytically with the parameters quantum effect, magnetic field, porosity and permeability in the stratified fluids. It is found that the magnetic field and quantum effect have more stabilizing influence on Rayleigh-Taylor instability in presence of porous media. We have also found that the porosity has stabilizing influence, while permeability has destabilizing influence on Rayleigh-Taylor instability in presence of quantum effect.

In this paper we investigate the effect of surface tension on hydromagnetic Rayleigh-Taylor (R-T) instability of two incompressible superimposed fluids in a porous medium with suspended dust particles immersed in a uniform horizontal magnetic field. The relevant linearized perturbation equations have been solved using normal mode technique and the dispersion relation is derived analytically for the considered system. The dispersion relation is influenced by the simultaneous presence of medium porosity, suspended dust particles, permeability, magnetic field and surface tension. The onset criteria of R-T stability and instability are obtained and discussed. The growth rate of R-T instability is calculated numerically and is affected by the simultaneous presence of surface tension and magnetic field. The effects of various parameters on the growth rate of the R-T instability are discussed.