Asymptotic behavior of solutions to the compressible Navier-Stokes equations on the half space

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Stability of Planar Stationary Solutions to the Compressible Navier-Stokes Equation on the Half Space (2006, methodology): “The estimates for derivatives are obtained in principle by the energy method as in [3, 7].”
Optimal Decay Rate of the Compressible Navier–Stokes–Poisson System in $${\mathbb {R}^3}$$ (2008, methodology): “The long time decay rate of global solution in multidimensional half space or exterior domain is also investigated for the compressible Navier-Stokes equations by Kagei-Kobayashi [10, 11], Kobayashi-Shibata [16], and Kobayashi [15].”
Optimal Time-decay Estimates for the Compressible Navier–Stokes Equations in the Critical Lp Framework (2016, result): “Similar results have been established in some situations where the fluid domain is not Rd: the half-space or exterior domain cases have been investigated by Kagei and Kobayashi in [18, 19], Kobayashi in [20], and Shibata and Kobayashi in [21].”
Decay of Dissipative Equations and Negative Sobolev Spaces (2011, background): “These results were extended to the exterior problem [18, 17] or the half space problem [15, 16] or with an external potential force [5], but without the smallness of L1-norm of the initial perturbation.”