Asymptotic behavior of solutions to the full compressible Navier–Stokes–Korteweg equations in the half space

Qian, Yujie; Yin, Rong; Li, Yeping

doi:10.1016/j.aml.2022.108499

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…Kotschote [24,25,26] established the local existence, global existence and time-asymptotics of strong solution for the non-isentropic compressible NSK equations in a bounded domain with C 3 -boundary. About the stability of basic nonlinear wave patterns such as the discontinuity wave, viscous contact wave and the rarefaction wave of one dimensional compressible NSK equations, we can refer to [6,7,8,31,37] and the references therein.…”

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confidence: 99%

Low Mach number limit of the full compressible Navier-Stokes-Korteweg equations with general initial data

Hao,

Li,

Yin

2024

Dynamics of Partial Differential Equations

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In this paper, the low Mach number limit for the three-dimensional full compressible Navier-Stokes-Korteweg equations with general initial data is rigorously justified within the framework of local smooth solution. Under the assumption of large temperature variations, we first obtain the uniform-in-Mach-number estimates of the solutions in a ε-weighted Sobolev space, which establishes the local existence theorem of the three-dimensional full compressible Navier-Stokes-Korteweg equations on a finite time interval independent of Mach number. Then, the low mach limit is proved by combining the uniform estimates and a strong convergence theorem of the solution for the acoustic wave equations. This result improves that of [K.-J. Sha and Y.-P. Li, Z. Angew. Math. Phys., 70(2019), 169] for well-prepared initial data.

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