Differential and Integral Equations

Global well posedness for a two-fluid model

Yoshikazu Giga, Slim Ibrahim, Shengyi Shen, and Tsuyoshi Yoneda

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We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posedness of the system in both space dimensions two and three. Regardless of the size of the initial data, we first prove the global well-posedness of the Cauchy problem when the space dimension is two. However, in space dimension three, we construct global weak-solutions à la Leray, and we prove the local well-posedness of Kato-type solutions. These solutions turn out to be global when the initial data are sufficiently small. Our results extend Giga-Yoshida (1984) [8] ones to the space dimension two, and improve them in terms of requiring less regularity on the velocity fields.

Article information

Differential Integral Equations, Volume 31, Number 3/4 (2018), 187-214.

First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76W05: Magnetohydrodynamics and electrohydrodynamics 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]


Giga, Yoshikazu; Ibrahim, Slim; Shen, Shengyi; Yoneda, Tsuyoshi. Global well posedness for a two-fluid model. Differential Integral Equations 31 (2018), no. 3/4, 187--214. https://projecteuclid.org/euclid.die/1513652423

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