Local and Global Existence of Solutions to Initial Value Problems of Nonlinear KaupKupershmidt Equations

This paper is devoted to studying the initial value problems of the nonlinear KaupKupershmidt equations ut*a1u2ux2*3ux3*5ux5=0, (x, t) R 2, and ut*a2ux2ux2*3ux3*5ux5=0, (x, t) R 2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear KaupKupershmidt equations. The results show that a local solution exists if the initial function u 0(x) H s (R), and s 5/4 for the first equation and s 301/108 for the second equation.