GLOBAL SOLUTIONS OF A TWO-DIMENSIONAL RIEMANN PROBLEM FOR THE PRESSURE GRADIENT SYSTEM

doi:10.3934/cpaa.2021014

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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
发表期刊	COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
ISSN	1534-0392
卷号	20 期号:7-8 页码:2475-2503
摘要	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.
关键词	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
收录类别	SCI
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000684207400004
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59081
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Gui-qiang G.
作者单位	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
推荐引用方式 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.