TY - JOUR
T1 - On Local Wellposedness of the Schrödinger-Boussinesq System
AU - Shao , Jie
AU - Guo , Boling
JO - Journal of Partial Differential Equations
VL - 4
SP - 360
EP - 381
PY - 2022
DA - 2022/10
SN - 35
DO - http://doi.org/10.4208/jpde.v35.n4.5
UR - https://global-sci.org/intro/article_detail/jpde/21054.html
KW - Schrödinger-Boussinesq system, Cauchy problem, local wellposedness, low regularity.
AB - <p style="text-align: justify;">In this paper we prove that the Schrödinger-Boussinesq system with solution $(u,v,$&nbsp; $(-\partial_{xx})^{-\frac12} v_t)$ is locally wellposed in $ H^{s}\times H^{s}\times H^{s-1}$, $s\geqslant-{1}/{4}$. The local wellposedness is obtained by the transformation from the problem into a nonlinear Schrödinger 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}\times H^{s}\times H^{s-1}$, $s&gt;-{1}/{4}$ given by Farah.</p>