论文标题
在真空附近的全球经典解决方案，即通过发散导管的等质超音速流的初始限值问题
Global Classical Solutions Near Vacuum to the Initial-Boundary Value Problem of Isentropic Supersonic Flows through Divergent Ducts
论文作者
论文摘要
在本文中，我们研究了真空吸尘器附近的经典解决方案的全球存在和渐近行为，用于初始边界价值问题建模通过不同的导管等递质超音速流。管理方程是具有小参数的可压缩欧拉方程，可以将其写成具有非疾病源的Riemann不变性的双曲线系统。我们为全球存在的经典解决方案提供了一个新的结果，用于没有假设小数据的非遗留双曲线平衡定律的初始限值问题。这项工作基于局部存在，最大原理和统一的先验估计值，该估计值是通过广义宽松变换获得的。通过研究沿每个特征曲线和垂直线的黎曼不变性的行为，还显示了经典溶液的渐近行为。结果可以应用于n维压缩欧拉方程的球形对称溶液。提供数值模拟以支持我们的理论结果。
In this paper, we study the global existence and asymptotic behavior of classical solutions near vacuum for the initial-boundary value problem modeling isentropic supersonic flows through divergent ducts. The governing equations are the compressible Euler equations with a small parameter, which can be written as a hyperbolic system in terms of the Riemann invariants with a non-dissipative source. We provide a new result for the global existence of classical solutions to initial-boundary value problems of non-dissipative hyperbolic balance laws without the assumption of small data. The work is based on the local existence, the maximum principle and the uniform a priori estimates obtained by the generalized Lax transformations. The asymptotic behavior of classical solutions is also shown by studying the behavior of Riemann invariants along each characteristic curve and vertical line. The results can be applied to the spherically symmetric solutions to N-dimensional compressible Euler equations. Numerical simulations are provided to support our theoretical results.
