Asymptotic Limit Of Quantum Euler-Maxwell Equations

The combined quasi-neutral and non-relativistic limit of compressible quantum Euler–Maxwell equations for plasmas is studied in this thesis.For well-prepared initial data,it is shown that the smooth solution of compressible quantum Euler–Maxwell equations converges to the smooth solution of incompressible Euler equations by using the asymptotic expansion method with small parameters of the singular perturbation,the modulation energy method and and so on.Furthermore,the associated convergence rates are also obtained.The thesis is divided into four chapters:The first chapter first introduce compressible quantum Euler–Maxwell equations and present the convergence from the compressible quantum Euler–Maxwell equations to the incompressible Euler equations in a formal level.Then we describes the physical background of quantum Euler-Maxwell equation's asymptotic limit problems and the progress of the study.The second chapter gives the article used basic knowledge which provides the corresponding theoretical basis for later come to the conclusion.The third chapter mathematically proved strictly under well-prepared initial data,can prove that the smooth solution of compressible quantum Euler-Maxwell's equations converges to the smooth solution of incompressible Euler equations,and further get the associated convergence rates.The fourth chapter present the further prospect on the problem.