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Volume 5, Issue 2
Existence and Uniqueness of Smooth Solution for a Four-Waves Coupled System

Mingyue Lin & Jingjun Zhang

DOI: 10.12150/jnma.2023.377

J. Nonl. Mod. Anal., 5 (2023), pp. 377-393.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we consider a four-waves coupled system which describes the interaction between particles. Based on the uniform bound and the strong convergence property in the lower order norm, local existence and uniqueness of smooth solution are established by a limiting argument. Moreover, we show that the solution exists globally in the two-dimensional case under certain condition on the size for $L^2$ norm of the initial data.

  • Keywords

Existence and uniqueness, global solution, four-waves coupled system.

  • AMS Subject Headings

37L05, 35Q35, 35B44

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-377, author = {Lin , Mingyue and Zhang , Jingjun}, title = {Existence and Uniqueness of Smooth Solution for a Four-Waves Coupled System}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {2}, pages = {377--393}, abstract = {

In this paper, we consider a four-waves coupled system which describes the interaction between particles. Based on the uniform bound and the strong convergence property in the lower order norm, local existence and uniqueness of smooth solution are established by a limiting argument. Moreover, we show that the solution exists globally in the two-dimensional case under certain condition on the size for $L^2$ norm of the initial data.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.377}, url = {http://global-sci.org/intro/article_detail/jnma/21932.html} }
TY - JOUR T1 - Existence and Uniqueness of Smooth Solution for a Four-Waves Coupled System AU - Lin , Mingyue AU - Zhang , Jingjun JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 377 EP - 393 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.377 UR - https://global-sci.org/intro/article_detail/jnma/21932.html KW - Existence and uniqueness, global solution, four-waves coupled system. AB -

In this paper, we consider a four-waves coupled system which describes the interaction between particles. Based on the uniform bound and the strong convergence property in the lower order norm, local existence and uniqueness of smooth solution are established by a limiting argument. Moreover, we show that the solution exists globally in the two-dimensional case under certain condition on the size for $L^2$ norm of the initial data.

Lin , Mingyue and Zhang , Jingjun. (2023). Existence and Uniqueness of Smooth Solution for a Four-Waves Coupled System. Journal of Nonlinear Modeling and Analysis. 5 (2). 377-393. doi:10.12150/jnma.2023.377
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