Large-Time Behavior of Solutions to an Inflow Problem for the Compressible Navier–Stokes–Korteweg Equations in the Half Space

Asymptotic stability of the rarefaction wave to one-dimensional compressible Navier-Stokes-Korteweg equations under space-periodic perturbations

“…for any f ∈ H 1 (R), together with ( 27), directly implies the large time behavior of the solutions: (25). This completes the proof of Theorem 3.1.…”

“…Li, Chen and Luo [26], and Li and Luo [27] recently discussed the stability of the planar rarefaction wave for the multidimensional isentropic compressible NSK equations on the domain R×T 2 and R×T, respectively, where the periodic boundary conditions are imposed in their settings. For the initial boundary value problem, we can refer to [7,6] for the impermeable wall problem, to [16,25,29] for the inflow problem, and to [17,31,30] for the outflow problem, respectively. Finally, we also mention that some literature study the large-time behavior of solutions to the isentropic compressible NSK equations when the initial data are small perturbation near to the non-vacuum constant states, i.e., [35,36,37,40], etc.…”