The optimal decay rate of strong solution for the compressible Navier-Stokes equations with large initial data

In a recent paper (He et al., 2019), it is shown that the upper decay rate of global solution of compressible Navier-Stokes(CNS) equations converging to constant equilibrium state (1, 0) in H-1-norm is (1 + t)(- 34 (2p-1)) when the initial data is large and belongs to H-2(R-3) boolean AND L-p(R-3)(p epsilon [1, 2)). Thus, the first result in this paper is devoted to showing that the upper decay rate of the first order spatial derivative converging to zero in H-1-norm is (1+ t)(- 3/2 (1p - 12)-12.) For the case of p = 1, the lower bound of decay rate for the global solution of CNS equations converging to constant equilibrium state (1, 0) in L-2-norm is (1+ t)(-3/)4 if the initial data satisfies some low frequency assumption additionally. In other words, the optimal decay rate for the global solution of CNS equations converging to constant equilibrium state in L-2-norm is (1 + t)(- 3/4) although the associated initial data is large. (C) 2020 Elsevier B.V. All rights reserved.