We derive a local energy inequality for weak solutions of the three dimensional magnetohydrodynamic equations. Combining Biot–Savart law, interpolation inequalities and the local energy inequality, we prove a partial regularity theorem for suitable weak solutions. Furthermore, we obtain an improved estimate for the logarithmic Hausdorff dimension of the singular set of suitable weak solutions.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics