A stability of the steady flow of compressible viscous fluid with respect to initial disturbance (v(infinity) (not equal)0)

We consider a compressible viscous fluid with the velocity at infinity equal to a strictly non-zero constant vector in R3. Under the assumptions on the smallness of the external force and velocity at infinity, Novotny-Padula (Math. Ann. 1997; 308:439- 489) proved the existence and uniqueness of steady flow in the class of functions possessing some pointwise decay. In this paper, we study stability of the steady flow with respect to the initial disturbance. We proved that if H3-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time, which satisfies a uniform estimate on prescribed velocity at infinity and converges to the steady flow in Lq-norm for any number q(greater than or equal) 2.