Well-posedness and blow-up phenomena for a higher order shallow water equation

作者：Mu Chunlai; Zhou Shouming^*; Zeng Rong

来源：Journal of Differential Equations, 2011, 251(12): 3488-3499.

DOI：10.1016/j.jde.2011.08.020

• Higher order shallow water equation
• Well-posedness
• Global existence
• Blow-up

This paper deals with the Cauchy problem for a higher order shallow water equation y(t) + au(x)y + buy(x) = 0, where y := Lambda(2k)u equivalent to (I - partial derivative(2)(x))(k)u and k = 2. The local well-posedness of solutions for the Cauchy problem in Sobolev space H(s)(R) with s >= 7/2 is obtained. Under some assumptions, the existence and uniqueness of the global solutions to the equation are shown, and conditions that lead to the development of singularities in finite time for the solutions are also acquired. Finally, the weak solution for the equation is considered.

• 出版日期2011-12-15
• 单位重庆大学