The Optimal Time Decay Of Solutions To The Cauchy Problem For Two-fluid Euler-Maxwell Equations In The Besov Space

In this paper,we mainly study the optimal time-decay estimate of classical solutions to the Cauchy problem for two-fluid Euler-Maxwell equations in critical regularity space,which are divided into the following four chapters.In the first chapter,firstly,the physical background of the two-fluid Euler-Maxwell equations is given and the research status of the partial differential equation system is briefly summarized.Secondly,the research difficulties encountered in mathematics and the methods used to overcome these difficulties are expounded.Finally,the main conclusions of the paper are given.In the second chapter,in order to prove the main conclusions of this paper,some important analysis tools are reviewed,such as Littlewood-Paley decomposition theory,the definition,properties of Besov space and its non-linear estimate in Besov space etc.At the same time,some symbols in the paper are also given.In the third chapter,in order to facilitate the study of two-fluid Euler-Maxwell equations,the equations are represented as a nonlinear perturbation near the constant equilibrium state.Because of the asymmetric dissipation of the equations,the weak dissipative structure of"regularity loss"appears in the analysis.In order to overcome this difficulty,the L~p-L~q-L~r decay inequality and the square formula of Duhamel principle are used to establish the optimal time decay of the classical solution of Cauchy problem in critical Besov space.This is an open question left over from reference[1].Chapter 4 summarizes this paper and puts forward further prospects for research issues.