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Existence and Uniqueness of Smooth Solution for a Four-waves Coupled System
  
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KeyWord:Existence and uniqueness, global solution, four-waves coupled system
Author NameAffiliation
Mingyue Lin Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China 
Jingjun Zhang College of Data Science, Jiaxing University, Jiaxing, 314001, China 
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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 strong convergence property in lower order norm, local existence and uniqueness of smooth solution is established by a limiting argument. Moreover, we show the solution exists globally in two dimensional case under certain condition on the size for $L^2$ norm of the initial data.