Xuanji Jia, Christian Klingenberg, Yun-guang Lu, Qingyou Sun, Existence of entropy solutions to system of polytropic gas with a class of unbounded sources

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DOI: 10.23952/jnva.7.2023.3.08

Volume 7, Issue 3, 1 June 2023, Pages 437-448

Abstract. We study the global existence of entropy solutions to a gas dynamics system with a class of unbounded sources. By using the maximum principle, we obtain the uniform $L^{\infty}$ -estimates for the viscosity solutions. The key ingredient here is to introduce two suitable bounded functions to control the unbounded source terms. Then, with the aid of the compensated compactness theory, we prove the convergence of viscosity solutions and existence of global entropy solutions for any adiabatic exponent $\alpha >1$ .

How to Cite this Article:
X. Jia, C. Klingenberg, Y.G. Lu, Q. Sun, Existence of entropy solutions to system of polytropic gas with a class of unbounded sources, J. Nonlinear Var. Anal. 7 (2023), 437-448.