Abstract
Study on supersonic flow around a given body is one of the main physical background of quasilinear hyperbolic system of conservation laws, as well as the main motivation of studing it. Generally speaking, when a supersonic flow attacks a given body, there will appear a shock front ahead of the body. If the body has a blunt head, the shock in front of it is detached. Otherwise, if the head of the body is sharp, then the shock can be attached on the head [3 22 27]. Here the main problem is to determine the location of the shock and the flow field in between the shock and the surface of the body. When the body has wing shape, the local existence of the solution and its some global property has been established in [11 24 14] for the wings with constant sections and in [4] for the wings with variable sections. When the body is a pointed body, a well known result is the case of a uniform supersonic flow past a circle cone with its axis parallel to the direction of the flow. However, in general case, the interaction of many factors, such as nonlinearity, multi-dimension, free boundary and the singularity caused by the tip of the pointed body let the problem become quite complicated. Therefore, the problem is open in the past 50 years, even though there has been great progress in the study of quasilinear hyperbolic system of conservation laws, particularly in one space dimensional case.
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Chen, S. (2001). Study on Supersonic Flow Past a Pointed Body. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 140. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8370-2_25
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DOI: https://doi.org/10.1007/978-3-0348-8370-2_25
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