We prove the stability of a planar contact discontinuity without shear, a family of special discontinuous solutions for the three-dimensional full Euler system, in the class of vanishing dissipation limits of the corresponding Navier–Stokes–Fourier system. We also show that solutions of the Navier–Stokes–Fourier system converge to the planar contact discontinuity when the initial datum converges to the contact discontinuity itself. This implies the uniqueness of the planar contact discontinuity in the class that we are considering. Our results give an answer to the open question, whether the planar contact discontinuity is unique for the multi-D compressible Euler system. Our proof is based on the relative entropy method, together with the theory of a-contraction up to a shift and our new observations on the planar contact discontinuity.

在相应的Navier–Stokes–Fourier系统的消失耗散极限类别中，我们证明了无剪切力的平面接触不连续性的稳定性，这是三维完整欧拉系统的特殊不连续性解决方案的一族。我们还表明，当初始基准面收敛到接触不连续点本身时，Navier–Stokes–Fourier系统的解收敛到平面接触不连续点。这意味着我们正在考虑的类别中平面接触不连续性的唯一性。我们的结果回答了一个悬而未决的问题，即平面接触不连续性对于多维可压缩Euler系统是否是唯一的。我们的证明是基于相对熵方法以及a的理论收缩直至移位，以及我们对平面接触不连续性的新观察。