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The zero-velocity limit solutions of the Navier-Stokes equations of compressible fluid revisited. (English) Zbl 1011.35102

The paper deals with the time-dependent Navier-Stokes equations. For an isentropic fluid flow driven by a potential force, the set of the so-called rest states (zero-velocity stationary solutions) is investigated. If the potential is locally Lipschitz continuous and the upper level sets are connected then the problem possesses at most two distinct solutions with given mass and total energy.

MSC:

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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