- Let . If , are free and solutions respectively, then one can control in if and only if
- (Parallel interactions)
- (Lack of smoothing)
- (Frequency cancellation)
- (No double endpoints) .
See FcKl2000. Null forms can also be handled by identities such as
- Some bilinear Strichartz estimates are also known. For instance, if , , are as in the linear Strichartz estimates , are solutions, then
as long as FcKl2000. Similar estimates for null forms also exist Pl2002; see also TaVa2000b, Ta2001b.