On Cauchy Problem Of Nonlinear Wave Equations

The aim of this paper is to deal with the well-posedness of global or local solutions for two kinds of nonlinear wave equations. In chapter 2, we consider the Cauchy problem for the following Boussinesq equationin Sobolev space C([0,T], Hs+1(R)) C1([0, T],Hs(R)).If /(M) satisfies certain conditions, we get the existence anduniqueness of the global solution for problem (1). In chapter 3, we study the following Boussinesq equationThe well-posedness of the global solutions for equation (2) is established . And a long time asymptotic solution of equation (2) is obtained in the same Sobolev space as that in chapter 1.Finally, we aim at the study of the Cauchy problem for the following Ostrovsky equationThe well-posedness of the local solution for equation (3) is present in Sobolev space which is different from that of chapter 1.