Gravitational instability of a composite system

The problem of instability arising in a composite system consisting of an infinitely conducting hydromagnetic fluid interacting through gravitational forces with one or more than one neutral gas, is investigated, allowing for a possible relative streaming between the component fluids. Instability criteria are derived for special cases of a two-component (static or relatively streaming) system and for a three-component system consisting of two gases contra-streaming in the presence of a stationary background gas. It is found that for a static system only one unstable mode exists for wave numbers less than a critical value given by the square root of the sum of the squares of the Jeans's wave numbers for individual gases. However, for a configuration, where components are endured with characteristic streaming speeds, there are present simultaneously more than one unstable modes.