PPT Slide
Weak GWP for small H1 initial data.
Under reasonable geometric
assumptions on M, have global
regularity for n = 2.
Step I) Reduction to small energy
Step II) Small energy implies Global Regularity
NONLINEAR RELATIVISTIC FIELD THEORIES
?I + ?IJK (?) Q0(?J,?K ) = 0
sc = n/2
Subcritical n = 1
Critical n = 2
Supercritical n ? 3
Need to go beyond bilinear estimates through an iterative approach.
Cannot be done by simple iterations.
Ex: f ? H1(R2) ? eif ? H1 (R2)
but f k ? H1 (R2) for k > 1.