Non-isentropic Hydrodynamic Models For Two-carrier Plasmas:Global Well-posedness

In this thesis, we are concerned with some analysis on hydrodynamic model. We prove the global existence of non-isentropic hydrodynamic models for two-carrier plasmas. Precisely, the thesis is divided into five chapters.In the first chapter, we give the background and state the development of the hydrodynamic model. Then we show some difficulties during this work and the methods to overcome these difficulties. Finally we give main results of this article.In the second chapter, we briefly introduce Besov spaces as well as some useful properties forthis kind of spaces.In the third chapter, we get the local existence and blow-up criterion of classical solution to the Cauchy problem in non-isentropic hydrodynamic models for two-carrier plasmas.In the fourth chapter, we employ energy methods to construct the nonlinear energy estimates to the hydrodynamic model. Besides, we obtain the global existence of classical solution with the help of a different energy estimate when the initial data is small under certain norms. Precisely, we first make energy estimates on the dissipative variable, then perform gradient estimates on the degenerate variable. Finally, combining these estimates above, we get the expected resultsIn the fifth chapter, we give a further outlook of the research problem.