Robin Young

Robin Young studies nonlinear waves and their interactions in hyperbolic systems of conservation laws, particularly the equations of fluid dynamics and classical mechanics. When nonlinearity is present, shock waves generically form, and these waves and their interactions lead to beautiful and complicated wave patterns. Young studies the nature and evolution of solutions by identifying ordering principles and resonances in these wave patterns. These studies reveal several intriguing and unexpected phenomena, such as amplitude blowup, vacuums and periodicity of solutions.

In his most recent work, together with Blake Temple, Young has proved the existence of a large class of nonlinear sound waves, which are smooth, time-periodic oscillatory solutions of the compressible Euler equations.  This work resolves a 175 year old paradox regarding sound waves versus shock waves, and also provides the first rigorous justification of  Acoustics, which is the study of sound using the linear wave equation.