Abstract
A model of two-phase isothermal ideal fluid is investigated by methods of the symmetry group theory. Different types of submodels are obtained for this model with respect to 3-dimensional subalgebras: invariant and partially invariant submodels. All invariant submodels are integrated. Ten subalgebras of the symmetry algebra are considered. Only these subalgebras generate barochronous motions of two-phase fluid. Many new exact solutions of two-phase fluid mechanics are found. They describe different motions of two-phase fluid, such as homogeneous motions, Galileo invariant motions and the motions with linear field of velocities. Two applications of the solutions are presented.
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