Geodesic
Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid
Applications of Mathematics, Tome 33 (1988) no. 5, pp. 389-409
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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.
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.
DOI : 10.21136/AM.1988.104319
Classification : 35A05, 35D05, 35Q10, 35Q30, 76N10
Keywords: Navier-Stoke equations; method of a discretization in time; global existence of weak solutions; mixed initial-boundary value problem; viscous compressible fluid 
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Neustupa, Jiří. Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid. Applications of Mathematics, Tome 33 (1988) no. 5, pp. 389-409. doi: 10.21136/AM.1988.104319

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