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March/April 2018 Global well posedness for a two-fluid model
Slim Ibrahim, Shengyi Shen, Tsuyoshi Yoneda, Yoshikazu Giga
Differential Integral Equations 31(3/4): 187-214 (March/April 2018).

Abstract

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.

Citation

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Slim Ibrahim. Shengyi Shen. Tsuyoshi Yoneda. Yoshikazu Giga. "Global well posedness for a two-fluid model." Differential Integral Equations 31 (3/4) 187 - 214, March/April 2018.

Information

Published: March/April 2018
First available in Project Euclid: 19 December 2017

zbMATH: 06837094
MathSciNet: MR3738195

Subjects:
Primary: 35Q30, 76N10, 76W05

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.31 • No. 3/4 • March/April 2018
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