  The global existence of classical solutions to strongly coupled parabolic
systems is shown to be equivalent to the availability of an iterative scheme
producing a sequence of solutions with uniform continuity in the BMO norms.
Amann's results on global existence of classical solutions still hold under
much weaker condition that their BMO norms do not blow up in finite time. The
proof makes use of some new global and local weighted Gagliardo-Nirenberg
inequalities involving BMO norms.
