Global Well-posedness And Blow Up Result For The Nonlinear Fractional Beam Equations

This dissertation is mainly devoted to consider the well-posedness of subcritical defocus-ing fractional Beam equations, well-posedness of critical defocusing fractional Beam equations with small initial data and the blow up phenomenon of focusing fractional Beam equations with negative energy.Frist, we give the background and introduce some elementary tools in the first chapter for convenience. Among these tools, someone are well-known, but we list them which are given simple proof or are only given results.Next, in the second chapter, we prove well-posedness of subcritical defocusing fractional Beam equations, well-posedness of critical defocusing fractional Beam equations with small initial data by using Strichartz estimates and contraction priciple. In this way, we treat the well-posedness of subcritical and citical defocusing Klein-Gordon equations and Beam equa-tions in a unified manner. Our result can be used to further study the difficult problem which is the scattering of subctitical and critical defocusing fracional Beam equations, especially for the case 1