Investigation of a problem governing a viscous compressible flow past a body in Hölder spaces

It is shown that the stationary exterior problem for the equations of notion of a viscous compressible liquid uniquely solvable in weighted Hölder spaces, if exterior forces and the value of velocity at infinity are sufficiently small. As a weight function, a power function $(1+|x|)^{-m}$, $m>0$ is taken. The proof, which is carried out by the method of decomposition, relies on the estimates of sindular integers and of solutions of the transport equations in weighted spaces.