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

作者：Xu Runzhang^*; Yang Yanbing; Liu Bowei; Shen Jihong; Huang Shaobin

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2015, 66(3): 955-976.

DOI：10.1007/s00033-014-0459-9

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

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.

• 出版日期2015-6
• 单位哈尔滨工程大学