Geodesic
A differential invariant solution of two-phase fluid dynamics equations
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 316-326

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A system of differential equations, which describes the dynamics of a gas suspension in an isothermal case is considered. It is derived the submodel of homogeneous medium movements, which are invariant with respect to Galilean shifts at the first coordinate. This submodel is a differentially invariant submodel with respect to a four-dimensional subalgebra with a basis of shift operators over all spatial coordinates and a Galilean transformation operator over the first coordinate. This submodel has been led to an involution and integrated. An exact solution of the system is found. A comparison of the solution with a known partially invariant solution is done. A group bundle of the system is constructed with respect to the subalgebra from the optimal system of subalgebras of the Lie algebra of the symmetry group for the system of two-phase fluid dynamics. This group bundle divides the system into two parts: automorphic and resolution. All solutions of the system are contained in the set of solutions of the group bundle and vice versa.
Keywords: symmetry group, differential invariant solution, two-phase fluid. 
@article{CHFMJ_2020_5_3_a5,
     author = {A. V. Panov},
     title = {A differential invariant solution of two-phase fluid dynamics equations},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {316--326},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a5/}
}
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A. V. Panov. A differential invariant solution of two-phase fluid dynamics equations. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 316-326. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a5/