Definition
Singular set of a weak velocity
The space-time points with no neighborhood on which the velocity is essentially bounded.
For a weak velocity on an open space-time set , call regular in the local boundedness sense if is essentially bounded on some neighborhood of contained in . The singular set is the complement of these regular points. Neighborhoods may be taken as balls for the parabolic metric.
Regularity convention
The regular set is open and the singular set is relatively closed. Partial regularity statements must specify their regularity convention. Turning boundedness into further smoothness uses an equation-specific theorem and force and pressure hypotheses; it is not part of this set-theoretic definition.