Global existence of solutions for incompressible magnetohydrodynamic equations
Volume 31 / 2004
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 $p\geq {7/3}$.
