报告题目：Nonlinear stability of composite waves involving boundary layers and Riemann waves for the inflow problem of the Navier-Stokes-Fourier system

报 告 人：黄旭山 博士后（延世大学）

报告时间：2026年7月8日（星期三）10：00-11：00

报告地点：6776永利集团114（小报告厅）  

校内联系人： 王国栋 副教授   联系方式：84708351-8503

报告简介: We investigate the large-time behavior of solutions to the one-dimensional inflow problem for the compressible Navier-Stokes-Fourier system. We prove the asymptotic stability of a composite wave consisting of a degenerate boundary layer, a large rarefaction wave, a viscous contact wave, and a viscous shock wave, up to a time-dependent dynamical shift. The result is established for small perturbations and small strengths of the boundary layer, contact wave, and shock wave, while the rarefaction wave is allowed to have arbitrarily large amplitude. The proof relies on the weighted relative entropy method, also known as the $a$-contraction framework. Compared with previous works, the presence of four distinct wave components leads to substantially more complicated wave interactions. Moreover, the large-amplitude rarefaction wave prevents a direct application of the weighted Poincar\'e inequality that is fundamental in the $a$-contraction analysis. The key observation is that, under the condition $1<\gamma\leq2$, the quantity $v^R\theta^R$ enjoys a suitable monotonicity property, which allows the weighted Poincar\'e-type inequality to be applied despite the large strength of the rarefaction wave. This provides the first stability result for such a general composite wave pattern in the inflow problem for the Navier-Stokes-Fourier equations.

报告人简介：黄旭山博士毕业于中国科学院数学与系统与科学研究院，目前在韩国延世大学从事博士后研究，研究工作涉及可压缩流体方程中的大时间行为和激波稳定性等。