Geodesic
Global existence of solutions for incompressible magnetohydrodynamic equations
Wisam Alame1 ; W. M. Zajączkowski2
1 Institute of Mathematics Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-956 Warszawa, Poland
Applicationes Mathematicae, Tome 31 (2004) no. 2, pp. 201-208 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Global-in-time existence of solutions for incompressible magnetohydrodynamic fluid equations in a bounded domain ${ \Omega }\subset {{\Bbb R}}^3$ with the boundary slip conditions is proved. The proof is based on the potential method. The existence is proved in a class of functions such that the velocity and the magnetic field belong to $W_p^{2,1}({ \Omega }\times (0,T))$ and the pressure $q$ satisfies $\nabla q\in L_p({ \Omega }\times (0,T))$ for $p\geq {7/3}$.
DOI : 10.4064/am31-2-5
Mots-clés : global in time existence solutions incompressible magnetohydrodynamic fluid equations bounded domain omega subset bbb boundary slip conditions proved proof based potential method existence proved class functions velocity magnetic field belong omega times pressure satisfies nabla omega times geq

Wisam Alame 1 ; W. M. Zajączkowski 2

1 Institute of Mathematics Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-956 Warszawa, Poland 
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     title = {Global existence
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     journal = {Applicationes Mathematicae},
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 magnetohydrodynamic equations
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Wisam Alame; W. M. Zajączkowski. Global existence
 of solutions for incompressible
 magnetohydrodynamic equations. Applicationes Mathematicae, Tome 31 (2004) no. 2, pp. 201-208. doi: 10.4064/am31-2-5

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