Well-posedness of Cauchy problems for Korteweg-de Vries-Benjamin-Ono equation and Hirota equation

摘要

The well-posedness of the Cauchy problems to the Korteweg-de Vries-Benjamin-Ono equation and Hirota equation is considered. For the Korteweg-de Vries-Benjamin-Ono equation, local result is established for data in H~s(R) (s >= -1/8). Moreover, the global well-posedness for data in L~2 (R) can be obtained. For Hirota equation, local result is established for initial data in H~s(s >= 1/4). In addition, the local solution is proved to be global in H~s (s >= 1) if the initial data are in H~s (s >= 1) by energy inequality and the generalization of the trilinear estimates associated with the Fourier restriction norm method.