Journal
JOURNAL OF MATHEMATICAL FLUID MECHANICS
Volume 21, Issue 2, Pages -Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00021-019-0431-8
Keywords
Compressible Navier-Stokes-Korteweg system; Besov space; well-posedness; time-decay
Funding
- JSPS [18K03368, 16H03945, 17K14216, 18J00557]
- Grants-in-Aid for Scientific Research [17K14216, 16H03945, 18J00557, 18K03368] Funding Source: KAKEN
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We consider the compressible Navier-Stokes-Korteweg system describing the dynamics of a liquid-vapor mixture with diffuse interphase. The global solutions are established under linear stability conditions in critical Besov spaces. In particular, the sound speed may be greater than or equal to zero. By fully exploiting the parabolic property of the linearized system for all frequencies, we see that there is no loss of derivative usually induced by the pressure for the standard isentropic compressible Navier-Stokes system. This enables us to apply Banach's fixed point theorem to show the existence of global solution. Furthermore, we obtain the optimal decay rates of the global solutions in the L2(Rd)-framework.
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