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On the Nonlinear Theory of Sound

Event Category:
Robin Young
UMass Amherst

We prove the existence of a large class of nonlinear sound waves,
which are smooth, time periodic, oscillatory solutions to the 3x3
compressible Euler equations, in one space dimension. Being
perturbations of solutions of a linear wave equation, these provide
the first rigorous justification for the centuries old theory of
Acoustics. In particular, Riemann's celebrated 1860 proof that
compressions always form shocks, appears to hold only for the
degenerate cases of isentropic and isothermal flows, and fails
under arbitrarily small perturbations of the entropy profile.

This is joint work with Blake Temple.


Thursday, April 6, 2023 - 4:00pm
LGRT 202