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Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid. (English) Zbl 0668.76074

The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally, a so called energy inequality is derived. The inequality is independent on the regularization used.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35Q30 Navier-Stokes equations
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References:

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