PPT Slide

Wave Maps

NONLINEAR RELATIVISTIC FIELD THEORIES

Known facts:

• Global Regularity n = 1.
• Small data Global Regularity, for all n.
• Examples of breakdown for nɮ.
• Global Regularity for spherically symmetric data n = 2.
• H1 - Weak solutions

• Well posed (WP) for s > sc
• Global well posed (GWP), small data, for s ? sc (Besov).

Bilinear Estimates

?I + ?IJK (?) Q0(?J,?K ) = 0

sc = n/2


Subcritical n = 1
Critical n = 2
Supercritical n ? 3

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