Two-dimensional steady supersonic exothermically reacting Euler flows with strong contact discontinuity over Lipschitz wall

TL;DR

This paper proves the global existence of supersonic reacting Euler flows with strong contact discontinuities over Lipschitz walls, providing estimates and validating quasi-one-dimensional approximations for such complex flow configurations.

Contribution

It establishes the global existence of solutions with strong contact discontinuities for 2D steady supersonic reacting Euler flows over Lipschitz walls, with rigorous approximation validation.

Findings

Global existence of entropy solutions with strong contact discontinuity.

Development of a modified Glimm-type functional for estimates.

Validation of quasi-one-dimensional approximation in the flow domain.

Abstract

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.