Investigation of the problem of the flow of a compressible viscous fluid past a bounded body in the hölder classes of functions

It is shown that the stationary exterior problem for the equations of motion of a viscous compressible fluid is uniquely solvable in weighted Hölder spaces if the exterior forces and the value of the 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 singular integrals and solutions of the transport equations in weighted spaces. Bibliography: 5 titles.