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Volume 35, Issue 4
On Local Wellposedness of the Schrödinger-Boussinesq System

Jie Shao & Boling Guo

DOI: 10.4208/jpde.v35.n4.5

J. Part. Diff. Eq., 35 (2022), pp. 360-381.

Published online: 2022-10

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  • Abstract

In this paper we prove that the Schrödinger-Boussinesq system with solution $(u,v,$  $(-\partial_{xx})^{-\frac12} v_t)$ 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}$, $s>-{1}/{4}$ given by Farah.

  • Keywords

Schrödinger-Boussinesq system, Cauchy problem, local wellposedness, low regularity.

  • AMS Subject Headings

35Q55, 35L70, 35A01, 76B15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

shaojiehn@foxmail.com (Jie Shao)

gbl@iapcm.ac.cn (Boling Guo)

  • BibTex
  • RIS
  • TXT
@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 = {

In this paper we prove that the Schrödinger-Boussinesq system with solution $(u,v,$  $(-\partial_{xx})^{-\frac12} v_t)$ 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}$, $s>-{1}/{4}$ given by Farah.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n4.5}, url = {http://global-sci.org/intro/article_detail/jpde/21054.html} }
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 -

In this paper we prove that the Schrödinger-Boussinesq system with solution $(u,v,$  $(-\partial_{xx})^{-\frac12} v_t)$ 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}$, $s>-{1}/{4}$ given by Farah.

Shao , Jie and Guo , Boling. (2022). On Local Wellposedness of the Schrödinger-Boussinesq System. Journal of Partial Differential Equations. 35 (4). 360-381. doi:10.4208/jpde.v35.n4.5
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