Unique strong solutions and V-attractor of a three dimensional globally modified magnetohydrodynamic equations

G. Deugoué; J. K. Djoko; A. C. Fouape; A. Ndongmo Ngana

doi:10.3934/cpaa.2020076

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2020, Volume 19, Issue 3: 1509-1535. Doi: 10.3934/cpaa.2020076

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Unique strong solutions and V-attractor of a three dimensional globally modified magnetohydrodynamic equations

1.
Department of Mathematics and Computer Science, University of Dschang, P. O. BOX 67, Dschang, Cameroon
2.
Department of Mathematics and Statistics, Florida International University, MMC, Miami, FL 33199, USA
3.
School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein 2000, Johannesburg, South Africa

^* Corresponding author
^* Corresponding author

Received: April 30, 2019

Revised: July 31, 2019

Published: February 2020

The first author is supported by the Fulbright Scholar Program Advanced Research and the Florida International University, 2019

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Abstract

In this paper, we provide a detailed investigation of the problem of existence and uniqueness of strong solutions of a three-dimensional system of globally modified magnetohydrodynamic equations which describe the motion of turbulent particles of fluids in a magnetic field. We use the flattening property to establish the existence of the global $ V $-attractor and a limit argument to obtain the existence of bounded entire weak solutions of the three-dimensional magnetohydrodynamic equations with time independent forcing.

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Mathematics Subject Classification: 76D05, 35Q35, 76D03, 35B41, 35D40.

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