Existence in the Large for Pressure-Gradient System

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 a...

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Bibliographic Details
Published inChinese annals of mathematics. Serie B Vol. 43; no. 4; pp. 509 - 522
Main Authors Zhang, Shuxin, Wang, Zejun
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022
Springer Nature B.V
Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Key Laboratory of Mathematical and High Performance Computing of Air Vehicles(NUAA),MIIT,Nanjing 210016,China
Subjects
Applications of Mathematics
Cauchy problems
Conservation laws
Coordinates
Mathematics
Mathematics and Statistics
Diperna’s conditions
BV space
Riemann problem
35B35
35A01
Pressure-gradient system
Glimm scheme
35B40
35L65
Diperna's conditions
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Summary: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.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-022-0343-4