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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.

Jeans Instability of Rotating Viscoelastic Fluid in the Presence of Magnetic Field