發(fā)布時間：2018-10-22 14:34

【摘要】：由于物理和力學領域的需要及其他應用領域相關(guān)研究的發(fā)展,很多時候所考察的問題最終歸結(jié)為一個數(shù)學問題來解決Euler方程組作為空氣動力學以及流體力學等學科中的重要模型,在數(shù)學上的研究也十分重要.本文主要研究了一維可壓縮Euler方程組的兩個模型：一維非等熵Chaplygin氣體動力學方程組和帶幾何結(jié)構(gòu)的一維等熵可壓縮Euler方程組.首先,考慮絕熱指數(shù)γ=-1時,非等熵情形下的一維可壓縮Euler方程組,即Chaplygin氣體方程組的Cauchy問題.在適當?shù)募僭O條件下,利用Gronwall不等式和特征線方法,得到Lagrange坐標下一維Chaplygin氣體方程組的整體經(jīng)典解.其次,考慮絕熱指數(shù)γ=3時,帶幾何機構(gòu)的一維可壓縮Euler方程組的L∞模的一致有界性.
[Abstract]:Due to the needs in the field of physics and mechanics and the development of related research in other fields of application, In many cases, the problem investigated is ultimately a mathematical problem to solve the Euler equations as an important model in aerodynamics and fluid dynamics, so the study of mathematics is also very important. In this paper, we study two models of one dimensional compressible Euler equations: one dimensional nonisentropic Chaplygin gas dynamics equations and one dimensional isentropic compressible Euler equations with geometric structure. Firstly, the Cauchy problem of Chaplygin gas equations is considered for one dimensional compressible Euler equations with adiabatic exponent 緯 = -1 and non-Isentropic. Under appropriate assumptions, the global classical solutions of one-dimensional Chaplygin gas equations in Lagrange coordinates are obtained by using the Gronwall inequality and the eigenline method. Secondly, the uniform boundedness of L 鈭，

本文編號：2287435