PPT Slide

• Energy estimates
• Strichartz inequalities
• Gauge conditions (Coulomb)
• Bilinear estimates

FACT 4: Null Condition

LWP for all s > sc n ? 4

WP for s > sc

GWP for s ? sc, small data

• Energy estimates

• Strichartz inequalities

• Bilinear estimates

? = F
F = ?(?) • Q(?, ?)

Q0(?,?) = - ?t ? ?t ? + ?i ?i ? ?i ?

Q?? (?,?) = ?? ? ?? ? + ?? ? ?? ?

Wave Maps

Yang-Mills

LWP for s > sc + 1/4, n = 3

GWP in the energy norm, n = 3

WORKING CONJECTURES - WP

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