The well-posedness of the Korteweg–de Vries–Benjamin–Ono equation

The well-posedness of the Cauchy problem to the generalized Korteweg–de Vries–Benjamin–Ono equation is considered. Local results for data in Hs (R) (s −1/8) and the global well-posedness for data in L2(R) are obtained if l = 2. Moreover, for l = 3, the problem is locally well-posed for data in Hs (s 1/4). The main idea is to use the Fourier restriction norm method.  2004 Elsevier Inc. All rights reserved