Study Of The Classic Solutions Of The Three Dimensional Compressible Euler Equations

The two problems of the compressible isentropic Euler equations are studied inin my thesis, including that with damping or without damping two cases. The researchresults have certain innovation, popularize the previous results. The full thesis is asfollows:Chapter1: The research progress of partial differential equations and Eulerequations are introduced, moreover, the research topic is also described.Chapter2: Blow-up of the exterior problem to the Non-damping isentropic Eulerequations is researched. Because of the particularity of the region, the structure of thefunctional is divided into more skill. And we construct the functionalF (t)=∫(x21)x ρudxx>1,to prove the classical solution to the initial-boundary value will blow up before afinite time under the assumption that the initial functional F (0)is large enough.Chapter3: Energy estimates are applied to study the global classical solution ofisentropic Euler equations with non-linear damping in bounded domain. If the initialdata is a small perturbation around a constant state, we prove that the global classicalsolution exist and it convergent to the constant state in an exponential decay rate.Chapter4: The work of full text is summarized, and some problems to be solvedare presented.