Free Dirac solutions have a one-dimensional div-curl structure that yields frequency-localized L2 bilinear null-form estimates, with an additional K/m gain for low-frequency same-branch pseudoscalar interactions.
The cubic Dirac equation: small initial data inH1(R3)
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Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations
Free Dirac solutions have a one-dimensional div-curl structure that yields frequency-localized L2 bilinear null-form estimates, with an additional K/m gain for low-frequency same-branch pseudoscalar interactions.