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On the Euler-Korteweg System with Free Boundary Condition

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Abstract

In this paper, we study the compressible Euler-Korteweg equations with free boundary condition in vacuum. Under physically assumptions of positive density and pressure, we introduce some physically quantities to show that the spreading diameter of regions grows linearly in time. This is an interesting result as one would expect that the capillary forces would prevent the boundary from spreading. Moreover, we construct a spherically symmetric global solution to support our theorem, followed by Sideris (J. Differ. Equ. 257:1–14, 2014).

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Acknowledgements

The authors are grateful to the referees and the editors whose comments and suggestions greatly improved the presentation of this paper. The work is partially supported by China NSF Grant No. 11271192, NSF of Jiangsu Province Grant No. BK20150794, Fundamental Research Funds for the Central Universities 2017B14314, PAPD of Jiangsu Higher Education Institutions and Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application.

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  1. Department of Mathematics, College of Sciences, Hohai University, Nanjing, 210098, China

    Tong Tang

  2. Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Hongjun Gao

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  1. Tong Tang
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  2. Hongjun Gao
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Correspondence to Tong Tang.

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Tang, T., Gao, H. On the Euler-Korteweg System with Free Boundary Condition. Acta Appl Math 150, 111–121 (2017). https://doi.org/10.1007/s10440-017-0097-2

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