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Global solutions to 1D compressible Navier-Stokes/Allen-Cahn system with density-dependent viscosity and free-boundary

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Abstract

This paper is concerned with the Navier-Stokes/Allen-Cahn system, which is used to model the dynamics of immiscible two-phase flows. We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form of η(ρ) = ρα. The existence of unique global H2m-solutions (m ∈ ℕ) to the free boundary problem is proven for when \(0 < \alpha < {1 \over 4}\). Furthermore, we obtain the global C∞-solutions if the initial data is smooth.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Shijin Ding, Yinghua Li & Yu Wang

Authors
  1. Shijin Ding
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  2. Yinghua Li
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  3. Yu Wang
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Correspondence to Yinghua Li.

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Conflict of Interest The authors declare no conflict of interest.

Additional information

Ding’s research was supported by the Key Project of the NSFC (12131010), the NSFC (11771155, 12271032) and the NSF of Guangdong Province (2021A1515010249, 2021A1515010303). Li’s research was supported by the NSFC (11971179, 12371205).

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Ding, S., Li, Y. & Wang, Y. Global solutions to 1D compressible Navier-Stokes/Allen-Cahn system with density-dependent viscosity and free-boundary. Acta Math Sci 44, 195–214 (2024). https://doi.org/10.1007/s10473-024-0111-5

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  • DOI: https://doi.org/10.1007/s10473-024-0111-5

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