REGULARITY OR BREAK-DOWN
The problem of possible break-down of solutions to interesting, non-linear, geometric and physical systems is:
Intimately tied to the basic mathematical question of understanding what we actually mean by solutions and, from a physical point of view, to the issue of understanding the very limits of validity of the corresponding physical theories.
the most conspicuous unifying problem; it affects all PDE
the most basic problem in PDE
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