Huo, Zhao Hui et Guo, Bo Ling, The Cauchy Problem for the Generalized Kortewegde VriesBenjaminOno Equation with Low Regularity Data, Acta mathematica Sinica. English series (Print) , 21(5), 2005, pp. 1191-1196
The Cauchy problem of the generalized Korteweg.de Vries.Benjamin.Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local wellposedness is obtained for data in Hs(R)(s>.34).. For k = 2, local result for data in Hs(R)(s.14) is obtained. For k = 3, local result for data in Hs(R)(s>.16) is obtained. Moreover, the solutions of generalized Korteweg.de Vries.Benjamin.Ono equation converge to the solutions of KdV equation if the term of Benjamin.Ono equation tends to zero.