论文标题
在Navier-Stokes-fourigh的一类零耗散限制中，平面触点的唯一性是3D可压缩欧拉系统的唯一性
Uniqueness of a planar contact discontinuity for 3D compressible Euler system in a class of zero dissipation limits from Navier-Stokes-Fourier system
论文作者
论文摘要
我们在没有剪切的情况下证明了接触不连续性的稳定性，这是一个特殊的不连续解决方案，用于三维完整的Euler系统，在相应的Navier-Stokes-Stokes-stokes-fourier System的消失耗散限制中。我们还表明，当初始基准收敛到触点不连续性本身时，Navier-Stokes-Fourier系统的解决方案会收敛到触点不连续性。这意味着我们正在考虑的班级中接触不连续性的独特性。我们的结果给出了一个开放问题的答案，即触点不连续性对于多D可压缩欧拉系统是否唯一。我们的证明基于相对熵方法，以及$ a $ contraction to to Shift的理论。
We prove the stability of contact discontinuities without shear, a family of special discontinuous solutions for the three-dimensional full Euler systems, 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 contact discontinuity when the initial datum converges to the contact discontinuity itself. This implies the uniqueness of the contact discontinuity in the class that we are considering. Our results give an answer to the open question, whether the 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.
