PPT Slide

GWP in the energy norm
WP for s > sc

sc = (n - 2) / 2

Subcritical n < 4
Critical n = 4
Supercritical n > 4

Yang-Mills

NONLINEAR RELATIVISTIC FIELD THEORIES

Known facts:

Global Regularity


Special breakdown solutions

CONJECTURE:

Global Regularity for all data, for n = 4.
Step I) Reduction to small energy

Step II) Small energy implies Global Regularity

Bilinear Estimates

CONJECTURE WP2:

Weak GWP for small initial data in the energy norm.

n ? 3

n > 4

n = 3

n ? 4

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