Vanishing viscosity with short wave long wave interactions for systems of conservation laws
Joćo Paulo Dias, Mario Figueira and Hermano Frid
Abstract: Motivated by Benney's general theory, we propose new models for short wave long wave interactions when the long waves are described by nonlinear systems of conservation laws. We prove the strong convergence of the solutions of the vanishing viscosity and short wave long wave interactions systems by using compactness results from the compensated compactness theory and new energy estimates obtained for the coupled systems. We analyse several of the representative examples such as scalar conservation laws, general symmetric systems, nonlinear elasticity, nonlinear electromagnetism.