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In this paper, we consider the global well-posedness problem of theisentropic compressible Navier-Stokes equations in the whole space $\R^N$ with$N\ge2$. In order to better reflect the characteristics of the dispersionequation, we make full use of the role of the frequency on the integrabilityand regularity of the solution, and prove that the isentropic compressibleNavier-Stokes equations admit global solutions when the initial data are closeto a stable equilibrium in the sense of suitable hybrid Besov norm. As aconsequence, the initial velocity with arbitrary $\dot{B}^{\fr{N}{2}-1}_{2,1}$norm of potential part $\Pe^\bot u_0$ and large highly oscillating are allowedin our results. The proof relies heavily on the dispersive estimates for thesystem of acoustics, and a careful study of the nonlinear terms.

Global solutions to the isentropic compressible Navier-Stokes equations with a class of large initial data