  In classical treatment of Maxwell equations, the initial and boundary
conditions are introduced by mathematical consideration rather than strictly
using the Maxwell equations. As a result, the initial and boundary conditions
are not logic consistent with the Maxwell equations. In fact, the boundary
problem of classical Maxwell equations is not solvable for general cases, if
the whole boundary fields are given. This problem is caused by implying the
divergence and the curl of a vector have no relations during introducing the
boundary condition. This research introduces new ideas and formulations to
solve this problem. The research shows that based on Chen S-R decomposition of
a rank-two tensor, this logical un-consistency can be discarded and, as a
consequence, the classical Maxwell equations are reformulated. According to the
reformulated Maxwell equations, the initial condition and boundary condition
have global effects. As an example, the London equations for superconductors
are deduced.
