The global existence of solutions to the equations of motion of a viscous gas with an artificial viscosity
Abstract
The system of equations of motion of a viscous barotropic fluid are examined. The system contains an artificial viscosity, which depends on the density (rho) of the fluid and is identically equal to zero for rho between 0 and rho2 (where rho2 is a given positive number). If rho2 is chosen sufficiently large, the system coincides with the NavierStokes equations, and the equation of continuity if the density has values that actually appear in real flows. 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.
 Publication:

Mathematical Methods in the Applied Sciences
 Pub Date:
 February 1991
 DOI:
 10.1002/mma.1670140203
 Bibcode:
 1991MMAS...14...93N
 Keywords:

 Barotropic Flow;
 Compressible Fluids;
 Equations Of Motion;
 Existence Theorems;
 Flow Equations;
 Viscous Fluids;
 Continuity Equation;
 Flow Distribution;
 NavierStokes Equation;
 Fluid Mechanics and Heat Transfer