@article{Zhao2022, 
author = {Xiangqing Zhao and Zhiwei Lv},
title = {Well-posedness of initial value problem of Hirota-Satsuma system in low regularity Sobolev space},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {6702-6710},
keywords = {{Hirota-Satsuma system, initial value problem, Fourier restrict norm method, local well-posed}},
url = {https://www.sciopen.com/article/10.3934/math.2022374},
doi = {10.3934/math.2022374},
abstract = {In this paper, we study the initial value problem of Hirota-Satsuma system:         {                                        u            t                    −          α          (                      u                          x              x              x                                +          6          u                      u            x                    )          =          2          β          v                      v            x                    ,                                    x          ∈                                    R                                ,                    t          ≥          0          ,                                                  v            t                    +                      v                          x              x              x                                +          3          u                      v            x                    =          0          ,                          x          ∈                                    R                                ,                    t          ≥          0          ,                                      u          (          0          ,          x          )          =          ϕ          (          x          )          ,                              v          (          0          ,          x          )          =          ψ          (          x          )          ,                          x          ∈                                    R                                ,                        where    α  ∈            R      ,    β  ∈            R      ;    u  =  u  (  x  ,  t  ),    v  =  v  (  x  ,  t  ) are real functions. Aided by Fourier restrict norm method, we show that    ∀  s  >  −      1    8   initial value problem (0.1) is locally well-posed in        H    s    (            R        )  ×      H          s      +      1        (            R        ) which improved the results of [7].}
}