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On the Nonlinear Theory of Sound

On the Nonlinear Theory of Sound

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.

Recording: https://umass-amherst.zoom.us/rec/share/emxzcDaYjfsEltOZchwAN7r8ebWxkUfY...

## Department of Mathematics and Statistics