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In this paper, we construct a family of global-in-time solutions of the 3-Dfull compressible Navier-Stokes (N-S) equations with temperature-dependenttransport coefficients (including viscosity and heat-conductivity), and showthat at arbitrary times {and arbitrary strength} this family of solutionsconverges to planar rarefaction waves connected to the vacuum as the viscosityvanishes in the sense of $L^\infty(\R^3)$. We consider the Cauchy problem in$\R^3$ with perturbations of the infinite global norm, particularly, periodicperturbations. To deal with the infinite oscillation, we construct a suitableansatz carrying this periodic oscillation such that the difference between thesolution and the ansatz belongs to some Sobolev space and thus the energymethod is feasible. The novelty of this paper is that the viscosity andheat-conductivity are temperature-dependent and degeneracies caused by vacuum.Thus the a priori assumptions and two Gagliardo-Nirenberg type inequalities areessentially used. Next, more careful energy estimates are carried out in thispaper, by studying the zero and non-zero modes of the solutions, we obtain notonly the convergence rate concerning the viscosity and heat conductivitycoefficients but also the exponential time decay rate for the non-zero mode.

Vanishing viscosity limit to the planar rarefaction wave with vacuum for  3-D full compressible Navier-Stokes equations with temperature-dependent  transport coefficients