The Kelvin–Helmholtz (K–H) instability in a magnetized nonuniform velocity sheared dusty plasma is investigated accounting for the effects of dust polarization force due to inhomogeneity in background plasma number densities. A three-component fluid model for dusty plasma is formulated considering Boltzmann electron/ion fluids and flowing magnetized dust fluids whose dynamics are affected due to the presence of dust polarization force. A dispersion relation for the K–H instability is derived by applying normal mode analysis on the linearized perturbation equations of the system. It is found that the polarization parameter dependent dust acoustic mode significantly modifies the dispersion relation of the K–H instability. The critical shear required to excite the K–H instability (S > Scrit) decreases with an increase in the dust polarization parameter and dust cyclotron frequency. The growth rate of the K–H instability is observed to be suppressed due to the presence of the dust polarization parameter. The results have been discussed for experimental magnetized dusty plasmas, which shows that under considered parametric limits, one cannot ignore the presence of dust polarization force on the excitation of the K–H instability in dusty plasmas. The astrophysical consequences are also discussed in Saturn’s E-ring in the limiting case of varying dust grain size.

The impact of galactic cosmic rays (CRs) in terms of CR pressure and parallel CR diffusion has been investigated on the low-frequency magnetohydrodynamic (MHD) waves and linear gravitational instability in the typical dusty plasma environment of molecular clouds (MCs). The dusty fluid model is formulated by combining the equations of the magnetized electrons/ions and dust particles, including the CR effects. The interactions between CR fluid and gravitating magnetized dusty plasma have been studied with the help of modified dispersion properties of the MHD waves and instabilities using the hydrodynamic fluid-fluid (CR-plasma) approach. CR diffusion affects the coupling of CR pressure-driven mode with dust-Alfvén MHD mode and causes damping in the MHD waves. It persists in its effect along the direction of the magnetic field and is diminished across the magnetic field. The phase speed diagram shows that for super-Alfvénic wave, the slow mode becomes the intermediate Alfvén mode. The fundamental Jeans instability criterion remains unaffected due to CR effects, but in the absence of CR diffusion, the effects of dust-acoustic speed and CR pressure-driven wave speed are observed in the instability criterion. It is found that CR pressure stabilizes while CR diffusion destabilizes the growth rates of Jeans instability and significantly affects the gravitational collapse of dusty MCs. The charged dust grains play a dominant role in the sub-Alfvénic and super-Alfvénic MHD waves and the collapse of MCs, triggering gravitational instability. The consequences have been discussed to understand the gravitational instability in the dense photodissociation regions (PDRs) of dusty MCs.