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Global Strong Solutions of a 2-D New Magnetohydrodynamic System

Abstract

The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg’s estimates for the stationary Stokes equation and Solonnikov’s theorem on Lp-Lq-estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses a global strong solution. In addition, the uniqueness of the global strong solution is obtained.

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Author information

Correspondence to Jiayan Yang.

Additional information

The work is supported by the Young Scholars Development Fund of SWPU (Grant No. 201899010079), the scientific research starting project of SWPU (Grant No. 2018QHZ029), the Natural Science Foundation of China (11771306), the National Nature Science Foundation of China (Key Program) (No. 51534006), Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and Its Applications (No. 18TD0013), Southwest Petroleum Univ. under Grant 2019CXTD08, Youth Science and Technology Innovation Team of Southwest Petroleum Univ. for Nonlinear Systems (No. 2017CXTD02), the Youth of Natural Science of SWMU (No. 2019ZQN146).

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Cite this article

Liu, R., Yang, J. Global Strong Solutions of a 2-D New Magnetohydrodynamic System. Appl Math 65, 105–120 (2020). https://doi.org/10.21136/AM.2020.0208-19

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Keywords

  • global strong solution
  • magnetohydrodynamics
  • Stokes equation
  • Lp-Lq-estimates

MSC 2010

  • 35Q35
  • 35D35
  • 35B65
  • 76W05
  • 35Q61