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Initial Boundary Value Problem for the 3D Magnetic-Curvature-Driven Rayleigh-Taylor Model

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Abstract

This article studies the initial-boundary value problem for a three dimensional magnetic-curvature-driven Rayleigh-Taylor model. We first obtain the global existence of weak solutions for the full model equation by employing the Galerkin’s approximation method. Secondly, for a slightly simplified model, we show the existence and uniqueness of global strong solutions via the Banach’s fixed point theorem and vanishing viscosity method.

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Acknowledgements

This work was finished when the first author was visiting the Institute of Applied Physics and Computational Mathematics. The first author wish to thank the hospitality of the Institute of Applied Physics and Computational Mathematics.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Xueke Pu

  2. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, China

    Boling Guo

Authors
  1. Xueke Pu
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  2. Boling Guo
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Corresponding author

Correspondence to Xueke Pu.

Additional information

This article is support in part by NNSF (11871172) and Natural Science Foundation of Guangdong Province of China (2019A1515012000).

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Pu, X., Guo, B. Initial Boundary Value Problem for the 3D Magnetic-Curvature-Driven Rayleigh-Taylor Model. Acta Math Sci 40, 529–542 (2020). https://doi.org/10.1007/s10473-020-0215-5

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  • DOI: https://doi.org/10.1007/s10473-020-0215-5

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