In this paper, we study the structurally nonlinear stability of supersoniccontact discontinuities in three-dimensional compressible isentropic steadyflows. Based on the weakly linear stability result and the $L^2$-estimatesobtained by the authors in J. Diff. Equ. 255(2013), for the linearized problemsof three-dimensional compressible isentropic steady equations at a supersoniccontact discontinuity satisfying certain stability conditions, we first derivetame estimates of solutions to the linearized problem in higher order norms byexploring the behavior of vorticities. Since the supersonic contactdiscontinuities are only weakly linearly stable, so the tame estimates ofsolutions to the linearized problems have loss of regularity with respect toboth of background states and initial data, so to use the tame estimates tostudy the nonlinear problem we adapt the Nash-Moser-H\"ormander iterationscheme to conclude that weakly linearly stable supersonic contactdiscontinuities in three-dimensional compressible steady flows are alsostructurally nonlinearly stable.
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机译：在本文中，我们研究了三维可压缩等熵稳态流中超音速接触间断的结构非线性稳定性。基于弱线性稳定性结果和J. Diff。作者的$ L ^ 2 $估计。等式255（2013），对于满足一定稳定性条件的超音速接触不连续性处的三维可压缩等熵稳态方程的线性化问题，我们首先通过探索涡度的行为推导了高阶范数线性化问题的解的估计估计。由于超音速接触不连续性仅具有较弱的线性稳定性，因此针对线性化问题的解决方案的驯服估计在背景状态和初始数据方面均失去规律性，因此要使用驯服估计来研究非线性问题，我们采用Nash-Moser- H·ormander迭代方案得出结论，三维可压缩稳定流中的弱线性稳定超声速接触不连续点在结构上也是非线性稳定的。
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