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 - <p style="text-align: justify;">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.</p>