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GLOBAL SOLUTIONS OF A TWO-DIMENSIONAL RIEMANN PROBLEM FOR THE PRESSURE GRADIENT SYSTEM
Chen, Gui-qiang G.1,2,3; Wang, Q. I. N.4; Zhu, S. H. E. N. G. G. U. O.1,5
2021-07-01
Source PublicationCOMMUNICATIONS ON PURE AND APPLIED ANALYSIS
ISSN1534-0392
Volume20Issue:7-8Pages:2475-2503
AbstractWe are concerned with a two-dimensional Riemann problem for the pressure gradient system that is a hyperbolic system of conservation laws. The Riemann initial data consist of four constant states in four sectorial regions such that two shocks and two vortex sheets are generated between the adjacent states. The solutions keep the four constant states and four planar waves outside the outer sonic circle in the self-similar coordinates, while the two shocks keep planar until meeting the outer sonic circle at two different points and then generate a diffracted shock to connect these points, whose location is apriori unknown. Then the problem can be formulated as a free boundary problem, in which the diffracted transonic shock is the one-phase free boundary to connect the two points, while the other part of the sonic circle forms a fixed boundary. We establish the global existence of a solution and the optimal Lipschitz regularity of both the diffracted shock across the two points and the solution across the outer sonic boundary. Then this Riemann problem is solved globally, whose solution contains two vortex sheets and one global shock containing the two originally separated shocks generated by the Riemann data.
KeywordTwo-dimensional Riemann problems global solutions pressure gradient system Euler equations hyperbolic conservation laws mixed type degenerate elliptic equations shocks transonic shock vortex sheets free boundary problem
DOI10.3934/cpaa.2021014
Indexed BySCI
Language英语
Funding ProjectUK Engineering and Physical Sciences Research Council[EP/L015811/1] ; Royal Society-Wolfson Research Merit Award (UK)[WM090014] ; National Natural Science Foundation of China[11761077] ; China Scholarship Council[201807035046] ; Key Project of Yunnan Provincial Science and Technology Department and Yunnan University[2018FY001-014] ; Royal Society-Newton International Fellowships[NF170015] ; Monash University-Robert Bartnik Visiting Fellowship ; Mathematical Institute, University of Oxford
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000684207400004
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/59081
Collection中国科学院数学与系统科学研究院
Corresponding AuthorChen, Gui-qiang G.
Affiliation1.Univ Oxford, Math Inst, Oxford OX2 6GG, England
2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
3.Chinese Acad Sci, AMSS, Beijing 100190, Peoples R China
4.Yunnan Univ, Dept Math, Kunming 650091, Yunnan, Peoples R China
5.Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China
Recommended Citation
GB/T 7714
Chen, Gui-qiang G.,Wang, Q. I. N.,Zhu, S. H. E. N. G. G. U. O.. GLOBAL SOLUTIONS OF A TWO-DIMENSIONAL RIEMANN PROBLEM FOR THE PRESSURE GRADIENT SYSTEM[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2021,20(7-8):2475-2503.
APA Chen, Gui-qiang G.,Wang, Q. I. N.,&Zhu, S. H. E. N. G. G. U. O..(2021).GLOBAL SOLUTIONS OF A TWO-DIMENSIONAL RIEMANN PROBLEM FOR THE PRESSURE GRADIENT SYSTEM.COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,20(7-8),2475-2503.
MLA Chen, Gui-qiang G.,et al."GLOBAL SOLUTIONS OF A TWO-DIMENSIONAL RIEMANN PROBLEM FOR THE PRESSURE GRADIENT SYSTEM".COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 20.7-8(2021):2475-2503.
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