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Axioms 2019, 8(2), 44; https://doi.org/10.3390/axioms8020044

Periodic Solution and Asymptotic Stability for the Magnetohydrodynamic Equations with Inhomogeneous Boundary Condition

1
Grupo de Matemática Aplicada, Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Av. Andres Bello 720, Casilla 447, Chillán 3780227, Chile
2
Departamento de Matemáticas, Universidad de La Serena, La Serena 1720236, Chile
3
Departamento de Matemáticas, Universidad de Atacama, Av. Copayapu 485, Casilla 240, Copiapó 1531772, Chile
4
Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica 1001003, Chile
*
Author to whom correspondence should be addressed.
Received: 6 December 2018 / Revised: 29 March 2019 / Accepted: 6 April 2019 / Published: 11 April 2019
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Abstract

We show, using the spectral Galerkin method together with compactness arguments, the existence and uniqueness of the periodic strong solutions for the magnetohydrodynamic-type equations with inhomogeneous boundary conditions. Furthermore, we study the asymptotic stability for the time periodic solution for this system. In particular, when the magnetic field h ( x , t ) is zero, we obtain the existence, uniqueness, and asymptotic behavior of the strong solutions to the Navier–Stokes equations with inhomogeneous boundary conditions. View Full-Text
Keywords: magnetohydrodynamic equations; periodic solutions magnetohydrodynamic equations; periodic solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kondrashuk, I.; Notte-Cuello, E.A.; Poblete-Cantellano, M.; Rojas-Medar, M.A. Periodic Solution and Asymptotic Stability for the Magnetohydrodynamic Equations with Inhomogeneous Boundary Condition. Axioms 2019, 8, 44.

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