Abstract
The main contribution of this paper is to provide a complete proof of the global weak entropy solution existence of the Cauchy problem for the Euler equations of one-dimensional compressible fluid flow and to correct the mistakes in the paper “Global weak solutions of the one-dimensional hydrodynamic model for semiconductors” (Math. Mod. Meth. Appl. Sci., 6(1993), 759–788). Our technique is the method of the artificial viscosity coupled with the theory of compensated compactness, where four families of Lax entropy-entropy flux pair are constructed by means of the classical Fuchsian equation.
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Acknowledgements
This paper is partially supported by the National Natural Science Foundation of China (Grant Nos. 12071106 and 12271483), and a Humboldt renewed research fellowship of Germany. The first author, Y.-G. Lu is very grateful to the colleagues in University of Wuerzburg for their warm hospitality.
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Lu, Yg., Klingenberg, C. & Tao, X. Global existence of entropy solutions for euler equations of compressible fluid flow. Math. Ann. (2024). https://doi.org/10.1007/s00208-024-02922-9
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DOI: https://doi.org/10.1007/s00208-024-02922-9