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Asymptotic profiles and convergence rate of the compressible fluid models of Korteweg type

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Abstract

In this paper, we consider the initial value problem for the compressible fluid models of Korteweg type in \({\mathbb {R}}^n(n\ge 3)\) and asymptotic profile of global solutions and the corresponding convergence rate are established. The structure of the nonlinear term plays a very important role in constructing asymptotic profile. The proof is based on the decay estimate of solutions operator, decay estimate and weighted decay estimate of global solutions.

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Acknowledgements

The work is partially supported by the NNSF of China (Grant No. 11871212) and the Basic Research Project of Key Scientific Research Project Plan of Universities in Henan Province (Grant No. 20ZX002).

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  1. School of Mathematics and statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450011, China

    Yinxia Wang & Yu-Zhu Wang

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  1. Yinxia Wang
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  2. Yu-Zhu Wang
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Correspondence to Yinxia Wang.

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Wang, Y., Wang, YZ. Asymptotic profiles and convergence rate of the compressible fluid models of Korteweg type. Z. Angew. Math. Phys. 71, 45 (2020). https://doi.org/10.1007/s00033-020-1269-x

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  • DOI: https://doi.org/10.1007/s00033-020-1269-x

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