Optimal decay estimate of mild solutions to the compressible Navier‐Stokes‐Korteweg system in the critical Besov space

In this paper, we consider the initial value problem for the compressible Navier‐Stokes‐Korteweg system in several space variables. Optimal decay estimate of mild solutions in the critical Besov spaces is established. The proof is based on the decay estimate of solutions operator in the low‐frequenc...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2018-12, Vol.41 (18), p.9592-9606
Main Authors: Wang, Yu‐Zhu, Wang, Yinxia
Format: Article
Language:English
Subjects:
Boundary value problems
Compressibility
compressible Navier‐Stokes‐Korteweg equations
Decay
decay estimate
Fluid dynamics
Fluid flow
fourth‐order wave equation with strong damping
Function space
mild solutions
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Summary:In this paper, we consider the initial value problem for the compressible Navier‐Stokes‐Korteweg system in several space variables. Optimal decay estimate of mild solutions in the critical Besov spaces is established. The proof is based on the decay estimate of solutions operator in the low‐frequency region and the energy estimate in the high‐frequency region.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5316