Global solutions of a two-dimensional Riemann problem for the pressure gradient system
Global solutions of a two-dimensional Riemann problem for the pressure gradient system
复制标题
压力梯度系统二维黎曼问题的全局解
DOI：
10.3934/cpaa.2021014
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发表时间：
2020-08
期刊：
影响因子：
--
通讯作者：
Shengguo Zhu
中科院分区：
文献类型：
--
作者：
Gui-Qiang G. Chen;Qin Wang;Shengguo Zhu
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.
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DOI：
10.4171/owr/2008/56
发表时间：
2004
期刊：
Oberwolfach Reports
影响因子：
--
作者：
Mathematisches Forschungsinstitut Oberwolfach;C. Dafermos;Randy LeVeque
通讯作者：
Mathematisches Forschungsinstitut Oberwolfach;C. Dafermos;Randy LeVeque
DOI：
10.1017/cbo9781139568050.009
发表时间：
--
期刊：
--
影响因子：
--
作者：
B. Riemann
通讯作者：
B. Riemann
影响因子：
3
作者：
S. Čanić;B. Keyfitz;Eun Heui Kim
通讯作者：
S. Čanić;B. Keyfitz;Eun Heui Kim
DOI：
--
发表时间：
2019-01
期刊：
arXiv: Analysis of PDEs
影响因子：
--
作者：
Myoungjean Bae;Gui-Qiang G. Chen;M. Feldman
通讯作者：
Myoungjean Bae;Gui-Qiang G. Chen;M. Feldman
影响因子：
4.9
作者：
L. Hörmander
通讯作者：
L. Hörmander