基于范德瓦尔斯状态方程的二维直管喷管中的声速-超声速射流
Sonic-supersonic jet flows from a straight two-dimensional nozzle with van der Waals equation of state
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中文总结 AI 辅助
研究基于范德瓦尔斯状态方程的二维直管喷管声速-超声速射流，通过特征分解和先验估计，建立了向真空中扩展的射流全局存在性，以及在特定静态大气条件下喷管出口附近射流的局部存在性。
中文摘要 AI 辅助
本文研究由稳态可压缩欧拉系统描述、基于范德瓦尔斯状态方程的二维直管喷管中的声速-超声速射流。规定喷管出口处的流动状态，假设周围介质为真空或低压静态大气。当喷管出口处流动达到声速状态时，控制方程变为退化双曲型，射流问题可表述为退化自由边界问题。喷管出口端点附近的奇异行为使分析更复杂。通过特征分解和合适的先验估计，我们建立了向真空中扩展的局部Lipschitz连续声速-超声速射流的全局存在性。此外，在存在压力低于喷管出口压力的静态大气时，我们证明了喷管出口附近声速-超声速射流的局部存在性。
英文摘要
This article concerns sonic-supersonic jet flows issuing from a two-dimensional straight nozzle described by the steady compressible Euler system under the van der Waals equation of state. The flow state is prescribed at the nozzle exit, while the surrounding medium is assumed to be either a vacuum or a static atmosphere with lower pressure. When the flow reaches the sonic state at the nozzle exit, the governing equations become degenerate hyperbolic and the resulting jet flow problem can be formulated as a degenerate free boundary problem. The analysis is further complicated by singular behavior near the endpoints of the nozzle exit. By employing characteristic decompositions and suitable a priori estimates, we establish the global existence of locally Lipschitz continuous sonic-supersonic jet flows expanding into a vacuum. Moreover, in the presence of a static atmosphere with pressure lower than that at the nozzle exit, we prove the local existence of sonic-supersonic jet flows near the nozzle exit.
