We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ρ0 L∞ is appropriate small and 1 < γ < 65.Here the initial density could have vacuum and we do not require that the initial energy is small.
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in the three space dimensions with general initial data which could be either vacuum or non-vacuum under the assumption that the viscosity coefficient μ is large enough.
