一维可压缩Euler方程组的两个模型
发布时间：2018-10-22 14:34
【摘要】：由于物理和力学领域的需要及其他应用领域相关研究的发展,很多时候所考察的问题最终归结为一个数学问题来解决Euler方程组作为空气动力学以及流体力学等学科中的重要模型,在数学上的研究也十分重要.本文主要研究了一维可压缩Euler方程组的两个模型：一维非等熵Chaplygin气体动力学方程组和带几何结构的一维等熵可压缩Euler方程组.首先,考虑绝热指数γ=-1时,非等熵情形下的一维可压缩Euler方程组,即Chaplygin气体方程组的Cauchy问题.在适当的假设条件下,利用Gronwall不等式和特征线方法,得到Lagrange坐标下一维Chaplygin气体方程组的整体经典解.其次,考虑绝热指数γ=3时,带几何机构的一维可压缩Euler方程组的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 纬 = -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，
本文编号：2287435
[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 纬 = -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，
本文编号：2287435
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