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

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 $\varepsilon$-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.

Keywords

Full compressible Navier-Stokes-Korteweg equation, low Mach number limit, general initial data, local smooth solution

2010 Mathematics Subject Classification

35B35, 35B40, 76N15

The full text of this article is unavailable through your IP address: 172.17.0.1

Received 24 April 2023

Published 21 May 2024