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September  2008, 10(4): 957-972. doi: 10.3934/dcdsb.2008.10.957

Very weak solutions for the magnetohydrodynamic type equations

Elder Jesús Villamizar-Roa 1, , Henry Lamos-Díaz 1, and  Gilberto Arenas-Díaz 1,

1. 

Universidad Industrial de Santander, Bucaramanga, Santander, A.A. 678, Colombia, Colombia, Colombia

Received  August 2007 Revised  March 2008 Published  August 2008

We consider the magnetohydrodynamic type equations with non-smooth Dirichlet boundary conditions for the velocity and the magnetic fields. We prove the existence of a kind of distributional solutions called very weak solutions and the continuous dependence of these solutions regarding the data; as a consequence, the uniqueness of very weak solutions is also obtained.
Keywords: Magnetohydrodynamic equations, very weak solutions, continuous dependence..
Mathematics Subject Classification: Primary:35Q30; Secondary:76D06, 35Q3.
Citation: Elder Jesús Villamizar-Roa, Henry Lamos-Díaz, Gilberto Arenas-Díaz. Very weak solutions for the magnetohydrodynamic type equations. Discrete & Continuous Dynamical Systems - B, 2008, 10 (4) : 957-972. doi: 10.3934/dcdsb.2008.10.957
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