The Classical Solutions Of The Compressible Euler Equations With Damping

Euler equations is an important part of the nonlinear partial differential equations.Especially, the Euler equations with damping has been one of the most active research fieldsin nonlinear partial differential equations. The aim of this thesis is to research the classicalsolutions of the Euler equations with damping. Results obtained in this thesis improve andextend many existing results. Full-text is divided into five chapters:Firstly, we introduce the research background and the research status of the Eulerequations with damping. Moreover, the main work of this thesis is described.Secondly, blowup for the solutions of the Euler equations with damping in n-dimensionalspace is discussed by structuring precise spherically symmetric solutionsu c t x.Furthermore, blowup for the radially symmetric solutions of the Euler equations withdamping in n-dimensional space is studied via the integration method. Then, the globalexistence and blowup for the rotated solutions consisting of some basic functions of a class ofEuler equations in3-dimensional space is investigated. As an extensive generalization, thehigh order estimation for the solutions of a class of Euler equations with damping in1-dimensional space is analyzed.At last, the main works and future works of this thesis are stated.