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The global existence of solutions to the equations of motion of a viscous gas with an artificial viscosity
Author(s) -
Neustupa JiřÍ
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140203
Subject(s) - barotropic fluid , mathematics , viscosity , viscous liquid , discretization , mathematical analysis , zero (linguistics) , flow (mathematics) , equations of motion , classical mechanics , mechanics , physics , geometry , thermodynamics , linguistics , philosophy
We deal with the system of equations of motion of a viscous barotropic fluid. The system contains an artificial viscosity, which depends on the density ρ of the fluid and is identically equal to zero for ρ ϵ 〈0, ρ 2 〉 (where, ρ 2 is a given positive number). If ρ 2 is chosen sufficiently large, the system coincides with the Navier–Stokes equations and the equations of continuity if the density has values that actually appear in real flows. The velocity is assumed to be equal to zero on the boundary of the flow field and the body force is not taken into account. Initial conditions need not be ‘small enough’. Applying the method of discretization in time, the existence of a weak solution on an interval of an arbitarary (but finite) length is proved and an estimate of the energy character is derived.