Description
Leonardo had a strong interest in mathematics (at the time, mostly
geometry
and simple algebraic equations). In the early part of his life, spent
in
Florence, Leonardo became interested in chaotic hydrodynamics (called
by
him, for the first time "turbulence"), a topic which will persist
throughout
his life. Examining the "turbulences" (eddies) in the river Arno he
found in
the late 1470 that the amplitude of the turbulence was decreasing very
slowly in time, until it would come to rest (within the surrounding
river).
This topic would remain dormant for close to 5 centuries, until in 1938
Tódór (Theodore) Kármán, triggered by Geoffrey Taylor, established that
the amplitude of the turbulence should decrease very slowly, indeed
like
an inverse power of the time elapsed. Three years later, Andrei
Kolmogorov
found an algebraic mistake in Kármán's calculation; Kolmogorov himself
found
another inverse power (5/7) of the time elapsed. This, likewise was
wrong.
In the talk we will present developments in a historical context and
connect
to recent progress on this topic. Very recently, we found that the law
of
decay of the amplitude need not be exactly an inverse of the time
elapsed.
Furthermore, more exotic laws of decay were obtained for "weak"
(distributional) solutions using a Nash-like construction.