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On the zero-velocity-limit solutions to the Navier-Stokes equations of compressible flow. (English) Zbl 0910.35097
Summary: We consider the zero-velocity stationary problem of the Navier-Stokes equations of compressible isentropic flow describing the distribution of the density \(\rho\) of a fluid in a spatial domain \(\Omega \subset \mathbb{R}^N\) driven by a time-independent potential external force \({\mathbf f} =\nabla F\). A sharp condition in terms of \(F\) is given for the problem to possess a unique nonnegative solution \(\rho\) having a prescribed mass \(m>0\).

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