## 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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