The global existence of solutions to the equations of motion of a viscous gas with an artificial viscosity

Abstract

Communicated by E. MeisterWe deal with the system of equations of motion of a viscous barotropic fluid. The system contains an artificial viscosity, which depends on the density p of the fluid and is identically equal to zero for p E (0, p 2 ) (where p2 is a given positive number). If p2 is chosen sufficiently large, the system coincides with the Navier-Stokes equations and the equation ofcontinuity 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 arbitrary (but finite) length is proved and an estimate of the energy character is derived.

Bipolar Barotropic Non-Newtonian Compressible Fluids

“…The behaviour of incompressible Newtonian fluids under assumptions of sufficient regularity and ρ > 0 was studied by Salvi and Straškraba [25]. Semigroup approach we can find in the work of Neustupa [21].…”