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Piston Problems of Two-Dimensional Chaplygin Gas

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Abstract

In this paper, the authors study the piston problem for the unsteady two-dimensional Euler system for a Chaplygin gas. The angle of the piston is allowed to vary in a wide range. The piston can be pushed forward into the static gas, or pulled back from the gas. The global existence of solution to the piston problem with any initial speed is established, and the structures of the global solutions are clearly described. The authors find that for the proceeding piston problem the front shock can be detached, attached or even adhere to the surface of the piston depending on the parameters of the flow and the piston; while for the receding problem the front rarefaction wave is always detached and the concentration will never occur.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Shuxing Chen

  2. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Aifang Qu

Authors
  1. Shuxing Chen
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  2. Aifang Qu
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Corresponding authors

Correspondence to Shuxing Chen or Aifang Qu.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11421061, 11571357, 11871218).

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Cite this article

Chen, S., Qu, A. Piston Problems of Two-Dimensional Chaplygin Gas. Chin. Ann. Math. Ser. B 40, 843–868 (2019). https://doi.org/10.1007/s11401-019-0164-2

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  • DOI: https://doi.org/10.1007/s11401-019-0164-2

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