Global existence of solutions for incompressible magnetohydrodynamic equations

Volume 31 / 2004

Wisam Alame, W. M. Zajączkowski Applicationes Mathematicae 31 (2004), 201-208 MSC: 35A05, 76W05, 76D03. DOI: 10.4064/am31-2-5

Abstract

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 $p\geq {7/3}$.

Authors

  • Wisam AlameInstitute of Mathematics
    Warsaw University of Technology
    Pl. Politechniki 1
    00-661 Warszawa, Poland
    e-mail
  • W. M. ZajączkowskiInstitute of Mathematics
    Polish Academy of Sciences
    /Sniadeckich 8
    00-956 Warszawa, Poland
    e-mail

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