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


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 $p\geq {7/3}$.


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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image