The Well-posedness Of The Degasperis-Procesi Equation In The Sobolev Space W^k,p(R)

Degasperis-Procesi(DP) equation is a kind of important mathematical physics equations, and the related research of DP equation has attracted much attention of the international academic field. In this paper, we study the Cauchy problem for the Degasperis-Procesi equation where u(x, t) is the horizontal component of the fluid velocity at time t in the spatial x-direction.In chapter 1, we introduce the DP equation and the research status. In Chapter 2, we employ the Kato's semigroup theory to establish the local well-posedness in the space Wk,p(R). The blow-up criterion for the DP equation is addressed in Chapter 3. A sufficient condition to guarantee the global solution is given in Chapter 4. Finally in Chapter 5, a weak limit result is established for the DP equation with linear dispersion term.