Global strong solutions of a 2-D new magnetohydrodynamic system

Ruikuan Liu; Jiayan Yang

Applications of Mathematics (2020)

  • Volume: 65, Issue: 1, page 105-120
  • ISSN: 0862-7940

Abstract

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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 L p - L q -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.

How to cite

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Liu, Ruikuan, and Yang, Jiayan. "Global strong solutions of a 2-D new magnetohydrodynamic system." Applications of Mathematics 65.1 (2020): 105-120. <http://eudml.org/doc/295010>.

@article{Liu2020,
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 $L^p$-$L^q$-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.},
author = {Liu, Ruikuan, Yang, Jiayan},
journal = {Applications of Mathematics},
keywords = {global strong solution; magnetohydrodynamics; Stokes equation; $L^p$-$L^q$-estimates},
language = {eng},
number = {1},
pages = {105-120},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global strong solutions of a 2-D new magnetohydrodynamic system},
url = {http://eudml.org/doc/295010},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Liu, Ruikuan
AU - Yang, Jiayan
TI - Global strong solutions of a 2-D new magnetohydrodynamic system
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 105
EP - 120
AB - 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 $L^p$-$L^q$-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.
LA - eng
KW - global strong solution; magnetohydrodynamics; Stokes equation; $L^p$-$L^q$-estimates
UR - http://eudml.org/doc/295010
ER -

References

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