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On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance. (English) Zbl 1051.76058
Summary: We consider a compressible viscous fluid under the action of arbitrary external force in $$R^3$$. First, an analysis of the linearized problem based on weighted $$L_2$$ method implies a condition on the external force for the existence and some regularity of the steady flow. Then we study the stability of steady flow with respect to an initial disturbance. We prove that, if $$H^3$$-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time.

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