Global Classical Solutions Of Compressible Euler-maxwell Equations

This work is concerned with some analysis on magnetic-hydrodynamic model ofsemiconductors．The author proves the global existence of classical solutions and large-timebehaviors for two fundamental systems of compressible Euler-Maxwell equations.The first part of this article the author gives the structures of the two models to study, thephysical background and significance of the research problem, as well as some of the difficultiesencountered in the process of doing this article, and for these difficulties the means through whichto overcome’s.The second part of the article the author briefly gives analysis based on some basic spaces,lemmas and basic nature that is used in the process of researching this article.In chapter3, the author study global well-posedness in critical Besov spaces for two-fluidEuler-Maxwell equations, which is different from the one-fluid case. We need to deal with thedifficulties mainly caused by the nonlinear coupling and cancelation between two carriers.Precisely, we first obtain the local existence and blow-up criterion of classical solution to theCauchy problem and periodic problem pertaining to data in Besov spaces with critical regularity.Furthermore, we construct the global existence of classical solutions with aid of a different energyestimate (in comparison with one-fluid case) provided the initial data is small under certain norms.Finally, we establish the large-time asymptotic behavior of global solutions near equilibrium inBesov spaces with relatively lower regularity.In chapter4, we study global existence of classical solutions of full Euler-Maxwell equations.The difference of full Euler-Maxwell equations and isentropic Euler-Maxwell equations is joinedby energy equation, so three conservation laws are include. We prove the global existence andlarge-time behavior of classical solutions to the full Euler-Maxwell equations in Chemin-Lernerspaces with critical regularity, which generalizes the recent results on isentropic Euler-Maxwellequations.The chapter5named of forecast is as the end of this article, the author suggests that someproblems need further study.