Plane and linear blow-up and source

Nonrelativistic equations of continuum mechanics are invariant with respect to space translations and Galilean translations. These symmetries form the 6-parameter group. The 3-dimensional subgroup of the general type containing the Galilean subgroup produces invariant solutions with the blow-up and the instantaneous source. The subgroup generating the solutions with the plane and linear blow-up and source or with both singularities together is considered. Gas particles move along a straight line for the invariant solutions and along plane curvilinear trajectories for the partially invariant solutions with special state equations. The classification of the state equations for these solutions with constant entropy is obtained. Simple solutions for the polytropic gas and the specific gas are found. •Invariant and partially invariant solutions of rank 1 for gas dynamics are obtained.•Particles move to the blow-up along the straight or curvilinear trajectories.•Blow-up and source can be a plane or a straight line.•The method of separation of the independent variables is developed.