具有特殊压力含有源项一维可压Euler方程组的弱解存在性

Global Weak Solution to a System of the Compressible Euler Equation with a Special Pressure and a Source

研究一类双曲系统——具有特殊压力含有源项的一维可压Euler方程组的Cauchy问题,应用补偿紧性理论和最大值原理,得到其有界弱解的整体存在性结果。所研究系统的齐次形式是1858年Earnshaw在研究等熵流体时第一次被推导出来,同时也被称为一位可压流的Euler方程组。其中的关键是用最大值原理得到相应的抛物方程组解的L∞估计,同时举出满足定理1条件(C1)–(C3)的一些具体源项。

The maximum principle and the theory of compensated compactness are applied to establish an existence theorem for global weak solutions to the Cauchy problem of the non-strictly hyperbolic system—a system of the compressible Euler equation with a special pressure and a source.Homogeneous system of this system was first derived by Earnshaw S.in 1858 for isentropic ow and is also called the Euler equations of one-dimensional compressible uid ow.The key is to obtain a priori-L∞estimate for solutions of the Cauchy problem for the related parabolic system by using the maximum principle and give some source terms satisfying the conditions（C1）–（C3） of Theorem 1.