Science China Mathematics

, Volume 61, Issue 3, pp 453–486 | Cite as

Local well-posedness of a multidimensional shock wave for the steady supersonic isothermal flow

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Abstract

In this paper, we prove the local existence, uniqueness and stability of a supersonic shock for the supersonic isothermal incoming flow past a curved cone. Major difficulties include constructing an appropriate solution and treating the Neumann boundary conditions and local stability condition.

Keywords

steady potential equation isothermal gas supersonic flow multidimensional conic shock local well-posedness local stability condition 

MSC(2010)

35L70 35L65 35L67 76N15 

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Notes

Acknowledgements

This work was supported by Scientific Research Fund of Nanjing Institute of Technology (Grant No. YKJ201339), National Natural Science Foundation of China (Grant Nos. 11371189 and 11101190) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. The author expresses his gratitude to Professor Yin Huicheng, Nanjing University, for suggesting the problem and giving many instructions. The author also thanks associate Professor Li Jun, Nanjing University, for his valuable suggestions.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsNanjing Institute of TechnologyNanjingChina
  2. 2.Department of Mathematics & Institute of Mathematical ScienceNanjing UniversityNanjingChina

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