Differential Invariants of Lie Pseudogroups in Mechanics of Fluids
نویسنده
چکیده
We present bases of differential invariants for Lie pseudogroups admitted by the main models of fluid mechanics. Among them infinite-dimensional parts of symmetry groups of Navier-Stokes equations in general (V.O. Bytev, 1972) and rotationally-symmetric (L.V. Kapitanskij, 1979) cases; stationary gas dynamics equations (M. Munk, R. Prim, 1947); stationary incompressible ideal magnetohydrodynamics (O.I. Bogoyavlenskij, 2000). Applications of the obtained bases to construction of differentially-invariant solutions and group foliations of the differential equations are demonstrated.
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