LGRT 202
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.