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Group classification of the three-dimensional equations describing flows offluids with internal inertia, where the potential function $W=W(\rho,\dot{\rho})$, is presented. The given equations include such models asthe non-linear one-velocity model of a bubbly fluid with incompressible liquidphase at small volume concentration of gas bubbles, and the dispersive shallowwater model. These models are obtained for special types of the function$W(\rho,\dot{\rho})$. Group classification separates out the function$W(\rho,\dot{\rho})$ at 15 different cases. Another part of the manuscript isdevoted to one class of partially invariant solutions. This solution isconstructed on the base of all rotations. In the gas dynamics such class ofsolutions is called the Ovsyannikov vortex. Group classification of the systemof equations for invariant functions is obtained. Complete analysis ofinvariant solutions for the special type of a potential function is given.

Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia