Skip to main content

Recent Results in Large Amplitude Monophase Nonlinear Geometric Optics

  • Chapter

Part of the book series: International Mathematical Series ((IMAT,volume 6))

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Bardos, What use for the mathematical theory of the Navier-Stokes equations, In: Mathematical Fluid Mechanics, Birkhauser, 2001, 1-25.

    Google Scholar 

  2. R. T. Chacon, Oscillations due to the transport of microstructures, SIAM J. Appl. Math. 48 (1988), no. 5, 1128-1146.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. Cheverry, Propagation of oscillations in real vanishing viscosity limit, Commun. Math. Phys. 247 (2004), no. 3, 655-695.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. Cheverry, Cascade of phases in turbulent flows, Bull. Soc. Math. Fr. 134 (2006), no. 1, 33-82.

    MATH  MathSciNet  Google Scholar 

  5. C. Cheverry, Sur la propagation de quasi-singularités [in French], Sémin. Équ. Dériv. Partielles, Éc. Polytech. Cent. Math., Palaiseau Sémin. 2005. 2004-2005, Exp. no. 8.

    Google Scholar 

  6. C. Cheverry, Counter-examples to the concentration-cancellation property, http://hal.ccsd.cnrs.fr.

    Google Scholar 

  7. C. Cheverry, O. Guès, and G. Métivier, Oscillations fortes sur un champ linéairement dégénéré [in French], Ann. Sci. Éc. Norm. Supér. (4) 36 (2003), no. 5, 691-745.

    Google Scholar 

  8. C. Cheverry, O. Guès, and G. Métivier, Large amplitude high frequency waves for quasilinear hyperbolic systems, Adv. Differ. Equ. 9 (2004), no. 7-8, 829-890.

    MATH  Google Scholar 

  9. J.-M. Delort, Existence de nappes de tourbillon en dimension deux, J. Am. Math. Soc. 4 (1991), no. 3, 553-586.

    Article  MATH  MathSciNet  Google Scholar 

  10. R.-J. DiPerna and A. J. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations, Commun. Math. Phys. 108 (1987), 667-689.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Friedlander, W. Strauss, and M. Vishik, Nonlinear instability in an ideal fluid, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 14 (1997), no. 2, 187-209.

    Article  MATH  MathSciNet  Google Scholar 

  12. I. Gallagher and L. Saint-Raymond, On pressureless gases driven by a strong inhomogeneous magnetic field, SIAM J. Math. Anal. 36 (2005), no. 4, 1159-1176.

    Article  MATH  MathSciNet  Google Scholar 

  13. O. Guès, Développement asymptotique de solutions exactes de systèmes hyperboliques quasilinéaires [in French], Asymptotic Anal. 6 (1993), 241-269.

    MATH  Google Scholar 

  14. O. Guès, Ondes multidimensionnelles ϵ-stratifiées et oscillations [in French], Duke Math. J. 68 (1992), no. 3, 401-446.

    Google Scholar 

  15. E. Grenier, On the nonlinear instability of Euler and Prandtl equations, Commun. Pure Appl. Math. 53 (2000), no. 9, 1067-1091.

    Article  MATH  MathSciNet  Google Scholar 

  16. J.-L. Joly, G. Métivier, and J. Rauch, Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves, Duke Math. J. 70 (1993), no. 2, 373-404.

    Article  MATH  MathSciNet  Google Scholar 

  17. J.-L. Joly, G. Métivier, and J. Rauch, Several recent results in nonlinear geometric optics, Progr. Nonlinear Differential Equations Appl., 21, Birkhauser Boston, Boston, MA, (1996).

    Google Scholar 

  18. A. J. Majda and A. L. Bertozzi, Vorticity and Incompressible Flow, Cambridge Univ. Press, Cambridge, 2002.

    MATH  Google Scholar 

  19. D. W. McLaughlin, G. C. Papanicolaou, and O. R. Pironneau, Convection of microstructure and related problems, SIAM J. Appl. Math. 45 (1985), no. 5, 780-797.

    Article  MATH  MathSciNet  Google Scholar 

  20. G. Lebeau, Non linear optic and supercritical wave equation, Bull. Soc. Roy. Sci. Liège 70 (2001), no. 4-6, 267-306.

    MATH  MathSciNet  Google Scholar 

  21. J. Rauch, Lectures on Geometric Optics, Providence, RI, 1999.

    Google Scholar 

  22. D. Serre, Oscillations non-linéaires hyperboliques de grande amplitude [in French], In: Nonlinear Variational Problems and Partial Differential Equations, Notes Math. Ser., 320, Longman Sci. Tech., Harlow, 1995, pp. 245-294.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Cheverry, C. (2008). Recent Results in Large Amplitude Monophase Nonlinear Geometric Optics. In: Bardos, C., Fursikov, A. (eds) Instability in Models Connected with Fluid Flows I. International Mathematical Series, vol 6. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75217-4_5

Download citation

Publish with us

Policies and ethics