Abstract
In this paper, the authors use Glimm scheme to study the global existence of BV solutions to Cauchy problem of the pressure-gradient system with large initial data. To this end, some important properties of the shock curves of the pressure-gradient system in the Riemann invariant coordinate system and verify that the shock curves satisfy Diperna’s conditions (see [Diperna, R. J., Existence in the large for quasilinear hyperbolic conservation laws, Arch. Ration. Mech. Anal., 52(3), 1973, 244–257]) are studied. Then they construct the approximate solution sequence through Glimm scheme. By establishing accurate local interaction estimates, they prove the boundedness of the approximate solution sequence and its total variation.
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This work was supported by the National Natural Science Foundation of China (No. 11671193).
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Zhang, S., Wang, Z. Existence in the Large for Pressure-Gradient System. Chin. Ann. Math. Ser. B 43, 509–522 (2022). https://doi.org/10.1007/s11401-022-0343-4
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DOI: https://doi.org/10.1007/s11401-022-0343-4