Abstract: | In this paper the Cauchy problem for a class of nonhomogenous Navier-Stokes equationsin the infinite cylinder is considered. We construct a unique local solution infor a class of nonhomogeneous Navier-Stokes equations provided that initialdata are in, where is an exponent determined by the structure of nonlinear termsand p,q are such that . Meanwhile under suitable conditions we also obtain thatprovided that initial data are sufficiently small. |