论文标题
ra尺测量解决方案的渗透压压缩欧拉的尤尔特方程的解决方案
Radon Measure Solutions to Riemann Problems for Isentropic Compressible Euler Equations of Polytropic Gases
论文作者
论文摘要
我们解决了ra量测量类别的多热气体的等渗压缩欧拉方程的riemann问题，而溶液则允许质量浓度。发现在满足过度压缩的熵条件的要求下：（i）有一个独特的Delta冲击解决方案，与具有两个强大的经典LAX冲击的情况相对应； （ii）对于经典Riemann溶液中包含冲击波和稀疏波的初始数据，或两次冲击，一个是弱的，有很多解决方案，每种解决方案都包含Delta Shock和稀疏波； （iii）对于经典熵弱解仅由稀疏波组成的情况，没有三角冲击。这些解决方案是自相似的。此外，对于最初不连续数据的不连续点的质量集中的广义黎曼问题，始终存在至少短时间内的独特的Delta冲击。它可以延长到全球解决方案。并非所有的溶液都是自相似的，这是由于浓缩点质量（粒子）的初始速度。阐明了是否满足过度压缩的熵条件的增量冲击溶液是否满足。这是对可压缩的欧拉（Euler）多变态气体系统构建单数测量解决方案的第一个结果，该系统严格夸张，其特征都是真正的非线性。我们还讨论了这些新解决方案的物理解释和应用。
We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures, and the solutions admit the concentration of mass. It is found that, under the requirement of satisfying the over-compressing entropy condition: (i) there is a unique delta shock solution, corresponding to the case that has two strong classical Lax shocks; (ii) for the initial data that the classical Riemann solution contains a shock wave and a rarefaction wave, or two shocks with one being weak, there are infinitely many solutions, each consists of a delta shock and a rarefaction wave; (iii) there is no delta shocks for the case that the classical entropy weak solutions consist only of rarefaction waves. These solutions are self-similar. Furthermore, for the generalized Riemann problem with mass concentrated initially at the discontinuous point of initial data, there always exists a unique delta shock for at least a short time. It could be prolonged to a global solution. Not all the solutions are self-similar due to the initial velocity of the concentrated point-mass (particle). Whether the delta shock solutions constructed satisfy the over-compressing entropy condition is clarified. This is the first result on the construction of singular measure solutions to the compressible Euler system of polytropic gases, that is strictly hyperbolic, and whose characteristics are both genuinely nonlinear. We also discuss possible physical interpretations and applications of these new solutions.
