PPT Slide

? - V’(?) = 0, n = 3, V = ? p+1

Subcritical p < 5
Critical p = 5
Supercritical p > 5

NONLINEAR RELATIVISTIC FIELD THEORIES

Known facts:

Global regularity


Strongly well posed for small H1 data

Weak H1 solutions

1

----

1+2

CONJECTURE:

There exist unstable solutions which break down in finite time. Global Regularity for generic data.

Nonlinear Wave Equations

No results in the supercritical case.

Numerical results suggest global regularity for all data.

p ? 5

p = 5

p > 5

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