Existence Of Global Weak Solution For Modified Novikov Equation

In this paper,we discuss the (1+1)D modified Novikov equation in the fol-lowing formwhere the variables x E R denote the one-dimensional space, t E R+represent the time and u(x, t) denote the wave speed or equivalent the height of water bottom to the free surface, and this equation change from the Novikov equation in the following formNovikov equation is one of the four important models describing the div-ing wave motion, the other three are the famous KDV equation, Cmassa-Holm Equation (CH equation) in the following form and the Degasperis-Procsi equation (DP equation) in the following formWe mainly study the Cauchy problem about model (0.1) and we obtain the global existence of the global weak solution when the Initial value satisfying some certain conditions.