International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 22, Pages 3609-3630

On the local well-posedness of a Benjamin-Ono-Boussinesq system

Ruying Xue

Department of Mathematics, Zhejiang University, Xixi Campus, Zhejiang, Hangzhou 310028, China

Received 30 March 2005; Revised 25 September 2005

Copyright © 2005 Ruying Xue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Consider a Benjamin-Ono-Boussinesq system ηt+ux+auxxx+(uη)x=0,ut+ηx+uux+cηxxxduxxt=0, where a, c, and d are constants satisfying a=c>0, d>0 or a<0, c<0, d>0. We prove that this system is locally well posed in Sobolev space Hs()×Hs+1(), with s>1/4.