Regularity results for weak solutions of the 3D MHD equations. (Q1433939)

The three-dimensional (3D) MHD equations with dissipation and resistance are studied in view of the regularity of general and axisymmetric solutions. A general weak solution is shown to be smooth if it satisfies Serrin condition. The regularity problem for weak solutions is analyzed in cylindrical coordinates. Using Gibbs' notion of dyadic product, the author shows that it is sufficient to impose certain conditions on components in cylindrical coordinates in order to obtain a regular weak solution of the problem.