Existence and Uniqueness of Smooth Solution for a Four-Waves Coupled System (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we consider a four-waves coupled system which describes the interaction between particles. Based on the uniform bound andthe strong convergence property in the lower order norm, local existence anduniqueness of smooth solution are established by a limiting argument. Moreover, we show that the solution exists globally in the two-dimensional caseunder certain condition on the size for $L^2$ norm of the initial data.