Year: 2022
Author: Boling Guo, Jie Shao, Boling Guo
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 360–381
Abstract
In this paper we prove that the Schrödinger-Boussinesq system with solution (u,v, (−∂xx)−12vt) is locally wellposed in Hs×Hs×Hs−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>-{1}/{4} given by Farah.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v35.n4.5
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 360–381
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Schrödinger-Boussinesq system Cauchy problem local wellposedness low regularity.