Abstract
This paper focuses on the multidimensional spherically symmetric full compressible Euler equations and constructs rigorously a family of global self-similar bounded weak solutions for all positive time to its initial value problem with constant initial data. The main approach is to reduce the full compressible Euler equations to an autonomous system of ordinary differential equations under the spherically symmetric and self-similar assumptions. We establish the detailed structures of solutions as well as their existence by analyzing carefully the properties of the integral curves of the autonomous ODE system.
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Acknowledgements
The authors would like to thank the anonymous reviewers for their careful work and comments that helped to improve the clarity of the paper. This work was supported by the Zhejiang Provincial Natural Science Foundation (No. LY17A010019) and National Science Foundation of China (Nos. 11301128, 11571088).
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Communicated by Syakila Ahmad.
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Hu, Y., Liu, J. Spherically Symmetric Solutions of the Full Compressible Euler Equations in \(R^N\). Bull. Malays. Math. Sci. Soc. 43, 1373–1390 (2020). https://doi.org/10.1007/s40840-019-00746-4
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DOI: https://doi.org/10.1007/s40840-019-00746-4