Bilinear wave estimates

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Bilinear estimates

  • Let . If , are free and solutions respectively, then one can control in 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 FcKl2000. Similar estimates for null forms also exist Pl2002; see also TaVa2000b, Ta2001b.