Luc TARTAR Compensated Compactness with more ... - ICMS

I hope that multi-scales H-measures (or better adapted improvements)
will permit to prove (or disprove) a few formal constructions
where a few scales interact, in particular in boundary
layers. There are two important problems for which one
has conjectured boundary layers with a few scales, one concerning
Joe KELLER’s GTD (geometric theory of diffraction),
and one concerning STEWARTSON’s (1925–1983) proposal of a
triple deck structure for some boundary layers in hydrodynamics,
but there are plenty of other problems where such ideas
should be tested, like for understanding the size of domains
and the movement of their (grain) boundaries.
A few years ago, Amit ACHARYA and I were quite puzzled to
hear someone (who had received the Nobel Prize in Physics in
the 1990s) mention in his talk that “biology is more difficult
than physics because problems in biology involve many scales,
while problems in physics always involve one scale”!
A few years before, I had heard a very interesting observation
in a talk by “Raj” RAJAGOPAL. Although he was working at
University of Pittsburgh at the time, I mostly met him abroad,
and his talk was given in Paris when the laboratory now called
LJLL (Laboratoire Jacques-Louis Lions) was still located in
Jussieu (before moving to Chevaleret, and back to Jussieu).
Raj started with an intuitive way to distinguish gases, liquids,
and solids: if one puts a small amount of gas into a container,
the gas soon fills the entire container; for a small amount of
liquid, it approximately keeps its volume and soon occupies all
the volume of the container below an horizontal plane, because
of gravity; for a small solid, it approximately keeps its shape,
and soon finds a position of equilibrium near the bottom of the
container, again because of gravity.
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