Lipschitz壁面上具有强接触间断的二维定常超音速粘性反应Euler流
Two-dimensional steady supersonic exothermically reacting Euler flows with strong contact discontinuity over Lipschitz wall
摘要：
本文在初始值和Lipschitz壁面斜率的全变差足够小时，建立了二维定常Euler方程在Lipschitz壁面上具有强接触间断的超音速熵解的整体存在性.本地和全球的估计和修改的Glimm型功能的精心设计。其次，通过证明弱解的平均值与准一维系统的解之差可以由初始数据的全变差和Lipschitz壁面斜率的平方来限定，严格证明了在壁面和强接触间断所限定的区域内准一维近似的有效性。本文提出的方法和技术对其他相关问题的解决也有一定的借鉴意义。
英文摘要：
In this paper, we established the global existence of supersonic entropy solutions with a strong contact discontinuity over Lipschitz wall governed by the two-dimensional steady exothermically reacting Euler equations, when the total variation of both initial data and the slope of Lipschitz wall is sufficiently small. Local and global estimates are developed and a modified Glimm-type functional is carefully designed. Next the validation of the quasi-one-dimensional approximation in the domain bounded by the wall and the strong contact discontinuity is rigorous justified by proving that the difference between the average of weak solution and the solution of quasi-one-dimensional system can be bounded by the square of the total variation of both initial data and the slope of Lipschitz wall. The methods and techniques developed here is also helpful for other related problems.
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