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Large Time Behavior of Global Strong Solutions to a Two-Phase Model with a Magnetic Field

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Abstract

In this paper, the Cauchy problem for a two-phase model with a magnetic field in three dimensions is considered. Based on a new linearized system with respect to (c − c∞, P − P∞, u, H) for constants c∞ ≥ 0 and P∞ > 0, the existence theory of global strong solution is established when the initial data is close to its equilibrium in three dimensions for the small H2 initial data. We improve the existence results obtained by Wen and Zhu in [40] where an additional assumption that the initial perturbations are bounded in L1-norm was needed. The energy method combined with the low-frequency and high-frequency decomposition is used to derive the decay of the solution and hence the global existence. As a by-product, the time decay estimates of the solution and its derivatives in the L2-norm are obtained.

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Wenjun Wang  (汪文军) & Zhen Cheng  (程珍)

Authors
  1. Wenjun Wang  (汪文军)
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  2. Zhen Cheng  (程珍)
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Correspondence to Wenjun Wang  (汪文军).

Additional information

The first author was supported by the National Natural Science Foundation of China (11871341 and 12071152).

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Wang, W., Cheng, Z. Large Time Behavior of Global Strong Solutions to a Two-Phase Model with a Magnetic Field. Acta Math Sci 42, 1921–1946 (2022). https://doi.org/10.1007/s10473-022-0512-2

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  • DOI: https://doi.org/10.1007/s10473-022-0512-2

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