Global classical solutions of compressible isentropic Navier-Stokes equations with small density

This paper concerns the Cauchy problem of compressible isentropic Navier-Stokes equations in the whole space R-3. First, we show that if rho(0) is an element of L-gamma boolean AND H-3, then the problem has a unique global classical solution on R-3 x [0, T] with any T is an element of (0, infinity), provided the upper bound of the initial density is suitably small and the adiabatic exponent gamma is an element of (1, 6). If, in addition, the conservation law of the total mass is satisfied (i.e., rho(0) is an element of L-1), then the global existence theorem with small density holds for any gamma > 1. It is worth mentioning that the initial total energy can be arbitrarily large and the initial vacuum is allowed. Thus, the results obtained particularly extend the one due to Huang-Li-Xin (Huang et al., 2012), where the global well-posedness of classical solutions with small energy was proved. (C) 2017 Elsevier Ltd. All rights reserved.