The Cauchy Problem for the Generalized Kortewegde VriesBenjaminOno Equation with Low Regularity Data

Authors
Huo, Zhao Hui Guo, Bo Ling
Citation
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
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
21
Issue
5
Year of publication
2005
Pages
1191 - 1196
Database
ACNP
SICI code
Abstract
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.