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On the ill-posedness of a weakly dispersive one-dimensional Boussinesq system

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Abstract

We study the Cauchy problem for a one-dimensional dispersive system of Boussinesq type which models weakly nonlinear long wave surface waves. We prove that such a system is ill-posed in H s(ℝ) for s < 0 in the sense that the solution does not depend continuously on the initial data. We also provide criteria for the formation of singularities.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Robin Ming Chen

  2. Department of Mathematics, University of Texas at Arlington, Arlington, TX, 76019-0408, USA

    Yue Liu

Authors
  1. Robin Ming Chen
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  2. Yue Liu
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Corresponding author

Correspondence to Robin Ming Chen.

Additional information

The work of R. M. Chen was partially supported by the NSF grant DMS-0908663.

The work of Y. Liu was partially supported by the NSF grant DMS-0906099 and the NHARP grant 003599-0001-2009.

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Chen, R.M., Liu, Y. On the ill-posedness of a weakly dispersive one-dimensional Boussinesq system. JAMA 121, 299–316 (2013). https://doi.org/10.1007/s11854-013-0037-7

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  • DOI: https://doi.org/10.1007/s11854-013-0037-7

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