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Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation

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Abstract

This paper is concerned with several aspects of the existence of global solutions and the formation of singularities for the Degasperis-Procesi equation on the line. Global strong solutions to the equation are determined for a class of initial profiles. On the other hand, it is shown that the first blow-up can occur only in the form of wave-breaking. A new wave-breaking mechanism for solutions is described in detail and two results of blow-up solutions with certain initial profiles are established.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas, Arlington, TX, 76019, USA

    Yue Liu

  2. Department of Mathematics, Zhongshan University, 510275, Guangzhou, China

    Zhaoyang Yin

  3. Institute for Applied Mathematics, University of Hanover, 30167, Hanover, Germany

    Zhaoyang Yin

Authors
  1. Yue Liu
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  2. Zhaoyang Yin
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Correspondence to Zhaoyang Yin.

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Communicated by A. Kupiainen

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Liu, Y., Yin, Z. Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation. Commun. Math. Phys. 267, 801–820 (2006). https://doi.org/10.1007/s00220-006-0082-5

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  • DOI: https://doi.org/10.1007/s00220-006-0082-5

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