KMS Of Academy of mathematics and systems sciences, CAS
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 Publication | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS |
ISSN | 1534-0392 |
Volume | 20Issue:7-8Pages:2475-2503 |
Abstract | We 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. |
Keyword | Two-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 |
DOI | 10.3934/cpaa.2021014 |
Indexed By | SCI |
Language | 英语 |
Funding Project | UK 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 Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000684207400004 |
Publisher | AMER INST MATHEMATICAL SCIENCES-AIMS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59081 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Chen, Gui-qiang G. |
Affiliation | 1.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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