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Vanishing Viscosity with Short Wave–Long Wave Interactions for Systems of Conservation Laws

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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 compensated compactness theory and new energy estimates obtained for the coupled systems. We analyze several of the representative examples, such as scalar conservation laws, general symmetric systems, nonlinear elasticity and nonlinear electromagnetism.

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Authors and Affiliations

  1. CMAF/UL and FC/UL, Universidade de Lisboa, Av. Gama Pinto, 2, 1649-003, Lisbon, Portugal

    João Paulo Dias & Mário Figueira

  2. Instituto de Matemática Pura e Aplicada,, IMPA Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, RJ, Brazil

    Hermano Frid

Authors
  1. João Paulo Dias
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  2. Mário Figueira
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  3. Hermano Frid
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Correspondence to Hermano Frid.

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Communicated by C. M. Dafermos

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Dias, J.P., Figueira, M. & Frid, H. Vanishing Viscosity with Short Wave–Long Wave Interactions for Systems of Conservation Laws. Arch Rational Mech Anal 196, 981–1010 (2010). https://doi.org/10.1007/s00205-009-0273-2

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  • DOI: https://doi.org/10.1007/s00205-009-0273-2

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