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Global existence and blowup of solutions for the multidimensional sixth-order “good” Boussinesq equation

  • Xu RunzhangEmail author
  • Yang Yanbing
  • Liu Bowei
  • Shen Jihong
  • Huang Shaobin
Article

Abstract

This paper is concerned with the Cauchy problem of solutions for some nonlinear multidimensional “good” Boussinesq equation of sixth order at three different initial energy levels. In the framework of potential well, the global existence and blowup of solutions are obtained together with the concavity method at both low and critical initial energy level. Moreover by introducing a new stable set, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level.

Mathematics Subject Classification

35Q35 

Keywords

Sixth-order multidimensional “good” Boussinesq equation Cauchy problem Global existence Blowup Arbitrarily positive initial energy 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Xu Runzhang
    • 1
    Email author
  • Yang Yanbing
    • 2
  • Liu Bowei
    • 1
  • Shen Jihong
    • 1
  • Huang Shaobin
    • 3
  1. 1.College of ScienceHarbin Engineering UniversityHarbinPeople’s Republic of China
  2. 2.College of AutomationHarbin Engineering UniversityHarbinPeople’s Republic of China
  3. 3.College of Computer Science and TechnologyHarbin Engineering UniversityHarbinPeople’s Republic of China

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