Refined L^2-decay estimate of solutions to a system of dissipative nonlinear Schroedinger equations

Authors

  • Naoyasu Kita Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto, Japan
  • Hayato Miyazaki Faculty of Education, Kagawa University, Kagawa, Japan
  • Yuji Sagawa Department of Mathematics, Osaka Metropolitan University, Osaka, Japan
  • Takuya Sato Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto, Japan

DOI:

https://doi.org/10.5564/jase-a.v5i1.3408

Keywords:

Nonlinear Schrodinger Equation, L^2-decay estimate, scale-invariant weighted estimate, weighted estimate

Abstract

We study the Cauchy problem of a system of dissipative nonlinear Schr¨odinger equations. Our target is to obtain a time-decay estimate of the solutions in $L^2$ without size-restriction on the initial data. By imposing high regularity and rapid spatial decay on the initial data, we find that the $L^2$-norm of the solutions decays at the rate of $O((\log t)^{−2/5})$ as $t \to \infty$. It is a refined decay-estimate, compared to former works. 

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Published

2024-12-01

How to Cite

[1]
N. Kita, H. Miyazaki, Y. Sagawa, and T. Sato, “Refined L^2-decay estimate of solutions to a system of dissipative nonlinear Schroedinger equations”, J. appl. sci. eng., A, vol. 5, no. 1, pp. 18–30, Dec. 2024.

Issue

Vol. 5 No. 1 (2024)

Section

Articles

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Copyright (c) 2024 Naoyasu Kita, Hayato Miyazaki, Yuji Sagawa, Takuya Sato

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