Mathematical modeling and dissipative structure for systems of magnetohydrodynamics with Hall effect

Shuichi Kawashima; Ryosuke Nakasato; Takayoshi Ogawa

doi:10.1142/S0218202522500427

Mathematical modeling and dissipative structure for systems of magnetohydrodynamics with Hall effect

Shuichi Kawashima, Ryosuke Nakasato^*, Takayoshi Ogawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is concerned with the mathematical modeling of electro-magneto-hydrodynamics and magnetohydrodynamics by taking account of the Hall effect. We discuss conservation laws, strict convexity of the negative entropy as a function of conserved quantities, and the associated energy form. Moreover, we investigate the dissipative structure and decay properties of the linearized systems as applications of the general theory developed in Umeda et al. [On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math. 1 (1984) 435-457] and Shizuta and Kawashima [Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249-275].

Original language	English
Pages (from-to)	1807-1878
Number of pages	72
Journal	Mathematical Models and Methods in Applied Sciences
Volume	32
Issue number	9
DOIs	https://doi.org/10.1142/S0218202522500427
Publication status	Published - 2022 Aug 1

Keywords

Hall effect
Magnetohydrodynamic systems
convex entropy
decay property
dissipative structure
hyperbolic-parabolic systems

ASJC Scopus subject areas

Modelling and Simulation
Applied Mathematics

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10.1142/S0218202522500427

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title = "Mathematical modeling and dissipative structure for systems of magnetohydrodynamics with Hall effect",

abstract = "This paper is concerned with the mathematical modeling of electro-magneto-hydrodynamics and magnetohydrodynamics by taking account of the Hall effect. We discuss conservation laws, strict convexity of the negative entropy as a function of conserved quantities, and the associated energy form. Moreover, we investigate the dissipative structure and decay properties of the linearized systems as applications of the general theory developed in Umeda et al. [On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math. 1 (1984) 435-457] and Shizuta and Kawashima [Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249-275].",

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author = "Shuichi Kawashima and Ryosuke Nakasato and Takayoshi Ogawa",

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T1 - Mathematical modeling and dissipative structure for systems of magnetohydrodynamics with Hall effect

AU - Kawashima, Shuichi

AU - Nakasato, Ryosuke

AU - Ogawa, Takayoshi

PY - 2022/8/1

Y1 - 2022/8/1

N2 - This paper is concerned with the mathematical modeling of electro-magneto-hydrodynamics and magnetohydrodynamics by taking account of the Hall effect. We discuss conservation laws, strict convexity of the negative entropy as a function of conserved quantities, and the associated energy form. Moreover, we investigate the dissipative structure and decay properties of the linearized systems as applications of the general theory developed in Umeda et al. [On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math. 1 (1984) 435-457] and Shizuta and Kawashima [Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249-275].

AB - This paper is concerned with the mathematical modeling of electro-magneto-hydrodynamics and magnetohydrodynamics by taking account of the Hall effect. We discuss conservation laws, strict convexity of the negative entropy as a function of conserved quantities, and the associated energy form. Moreover, we investigate the dissipative structure and decay properties of the linearized systems as applications of the general theory developed in Umeda et al. [On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math. 1 (1984) 435-457] and Shizuta and Kawashima [Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249-275].

KW - Hall effect

KW - Magnetohydrodynamic systems

KW - convex entropy

KW - decay property

KW - dissipative structure

KW - hyperbolic-parabolic systems

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Mathematical modeling and dissipative structure for systems of magnetohydrodynamics with Hall effect

Abstract

Keywords

ASJC Scopus subject areas

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