Existence in the Large for Pressure-Gradient System*

Citation:

Shuxin ZHANG,Zejun WANG.Existence in the Large for Pressure-Gradient System*[J].Chinese Annals of Mathematics B,2022,43(4):509~522
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Authors:

Shuxin ZHANG; Zejun WANG

Foundation:

National Natural Science Foundation of China (No. 11671193).
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.

Keywords:

Pressure-gradient system, Riemann problem, Diperna’s conditions,Glimm scheme, BV space

Classification:

35A01, 35B35, 35B40, 35L65
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