In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in com- pressible flow.The corresponding mathematical model is the well-known Euler system.With the Newton iteration procedure and energy e...In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in com- pressible flow.The corresponding mathematical model is the well-known Euler system.With the Newton iteration procedure and energy estimate,we give the local existence of the shock front solution to this problem.展开更多
The 1-D piston problem for the pressure gradient equations arising from the flux-splitting of the compressible Euler equations is considered. When the total variations of the initial data and the velocity of the pisto...The 1-D piston problem for the pressure gradient equations arising from the flux-splitting of the compressible Euler equations is considered. When the total variations of the initial data and the velocity of the piston are both sufficiently small, the author establishes the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength by employing a modified wave front tracking method.展开更多
研究了修正的Van der Waals气体Euler方程的活塞问题.利用Maxwell提出的等面积法则,将Van der Waals气体状态方程修正为与实际相符合,从而将方程从混合型转会化为双曲型.利用特征分析法,给出修正的Van der Waals气体Euler方程的Riemann...研究了修正的Van der Waals气体Euler方程的活塞问题.利用Maxwell提出的等面积法则,将Van der Waals气体状态方程修正为与实际相符合,从而将方程从混合型转会化为双曲型.利用特征分析法,给出修正的Van der Waals气体Euler方程的Riemann问题前向波的所有解,从而进一步给出了推拉活塞时气体的所有运动.展开更多
In this paper,the authors study the piston problem for the unsteady two-dimensional Euler system for a Chaplygin gas.The angle of the piston is allowed to vary in a wide range.The piston can be pushed forward into the...In this paper,the authors study the piston problem for the unsteady two-dimensional Euler system for a Chaplygin gas.The angle of the piston is allowed to vary in a wide range.The piston can be pushed forward into the static gas,or pulled back from the gas.The global existence of solution to the piston problem with any initial speed is established,and the structures of the global solutions are clearly described.The authors find that for the proceeding piston problem the front shock can be detached,attached or even adhere to the surface of the piston depending on the parameters of the flow and the piston;while for the receding problem the front rarefaction wave is always detached and the concentration will never occur.展开更多
基金Supported partially by NSFC Project 10131050 and NSFC Project 10271108
文摘In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in com- pressible flow.The corresponding mathematical model is the well-known Euler system.With the Newton iteration procedure and energy estimate,we give the local existence of the shock front solution to this problem.
基金supported by the National Natural Science Foundation of China(Nos.11626176,11701435)the Fundamental Research Funds for the Central Universities of China(Nos.2018IB015,2018IVB013)
文摘The 1-D piston problem for the pressure gradient equations arising from the flux-splitting of the compressible Euler equations is considered. When the total variations of the initial data and the velocity of the piston are both sufficiently small, the author establishes the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength by employing a modified wave front tracking method.
文摘研究了修正的Van der Waals气体Euler方程的活塞问题.利用Maxwell提出的等面积法则,将Van der Waals气体状态方程修正为与实际相符合,从而将方程从混合型转会化为双曲型.利用特征分析法,给出修正的Van der Waals气体Euler方程的Riemann问题前向波的所有解,从而进一步给出了推拉活塞时气体的所有运动.
基金supported by the National Natural Science Foundation of China(Nos.11421061,11571357,11871218)
文摘In this paper,the authors study the piston problem for the unsteady two-dimensional Euler system for a Chaplygin gas.The angle of the piston is allowed to vary in a wide range.The piston can be pushed forward into the static gas,or pulled back from the gas.The global existence of solution to the piston problem with any initial speed is established,and the structures of the global solutions are clearly described.The authors find that for the proceeding piston problem the front shock can be detached,attached or even adhere to the surface of the piston depending on the parameters of the flow and the piston;while for the receding problem the front rarefaction wave is always detached and the concentration will never occur.
