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The Global Existence of BV Solutions of the Isentropic p-System with Large Initial Data

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Abstract

In this paper, we study the global existence of BV solutions of the initial value problem for the isentropic p-system, where the state equation of the gas is given by P = Av−γ. For γ < 1, the general existence result for large initial data has not been obtained. By using the Glimm scheme, Nishida, Smoller and Diperna successively obtained the global existence results for (γ − 1)TV(v0(x),u0(x)) being small. In the present paper, by adopting a rescaling technique, we improve these results and obtain the global existence result under the condition that (γ −1)γ+1 (TV(v0(x)))γ−1 (TV(u0(x)))2 is small, which implies that, for fixed γ > 1, either TV(v0 (x)) or TV(u0 (x)) can be arbitrarily large.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Fei Wu  (吴菲), Zejun Wang  (王泽军) & Fangqi Chen  (陈芳启)

  2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, 211106, China

    Fei Wu  (吴菲), Zejun Wang  (王泽军) & Fangqi Chen  (陈芳启)

Authors
  1. Fei Wu  (吴菲)
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  2. Zejun Wang  (王泽军)
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  3. Fangqi Chen  (陈芳启)
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Corresponding author

Correspondence to Fangqi Chen  (陈芳启).

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Conflict of Interest

The authors declare no conflict of interest.

Zejun Wang was partially supported by the NSFC (11671193); Fangqi Chen was partially supported by the NSFC (12172166, 11872201).

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Wu, F., Wang, Z. & Chen, F. The Global Existence of BV Solutions of the Isentropic p-System with Large Initial Data. Acta Math Sci 43, 1668–1674 (2023). https://doi.org/10.1007/s10473-023-0414-y

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  • DOI: https://doi.org/10.1007/s10473-023-0414-y

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