On Local Wellposedness of the Schrodinger-Boussinesq System  

作　　者：SHAO Jjie GUO Boling 

机构地区：[1]Department of Mathematics,Nanjing University of Science and Technology,Nanjing210094,China [2]Institute of Applied Physics and Computational Mathematics,Beijing 100088,China [3]The Graduate School of China Academy of Engineering Physics,Beijing 100088,China

出　　处：《Journal of Partial Differential Equations》2022年第4期360-381,共22页偏微分方程（英文版）

摘　　要：In this paper we prove that the Schrodinger-Boussinesq system with solution(u,v,(-∂xx)-^(2/1)vt)is locally wellposed in H^(s)×H^(s)×Hs^(-1),s≥-1/4.The local wellposedness is obtained by the transformation from the problem into a nonlinear Schrodinger type equation system and the contraction mapping theorem in a suitably modified Bourgain type space inspired by the work of Kishimoto,Tsugawa.This result improves the known local wellposedness in H^(s)×H^(s)×H^(s-1),s>-1/4 given by Farah.

关 键 词：Schrodinger-Boussinesq system Cauchy problem local wellposedness low regularity. 

分 类 号：O175.27[理学—数学]