The well-posedness of three-dimensional Navier-Stokes and magnetohydrodynamic equations with partial fractional dissipation

Qibo Ma, Li Li

It is well-known that if one replaces standard velocity and magnetic dissipation by $(-\Delta {)}^{\alpha }u$ and $(-\Delta {)}^{\beta }b$ respectively, the magnetohydrodynamic equations are well-posed for $α\ge…