@Article{JPDE-35-360,
author = {Shao , Jie and Guo , Boling},
title = {On Local Wellposedness of the Schrödinger-Boussinesq System},
journal = {Journal of Partial Differential Equations},
year = {2022},
volume = {35},
number = {4},
pages = {360--381},
abstract = {<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>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v35.n4.5},
url = {http://global-sci.org/intro/article_detail/jpde/21054.html}
}