# Bilinear wave estimates

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- Let . If , are free and solutions respectively, then one can control fy in \dot X^{s,b} if and only if
- (Scaling)
- (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 FcKl-p. Similar estimates for null forms also exist Pl2002; see also TaVa2000b, [Ta-p4].