GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

National Natural Science Foundation of China [11001090]; Fundamental Research Funds for the Central Universities [11QZR16]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 parallel to rho(0)parallel to(L infinity) is appropriate small and 1 < gamma < 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small