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

Speaker: 黄旭山 博士  韩国延世大学

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

Language: Chinese

Time & Venue: 2026.07.15   10:30-11:30    思源楼S315

Abstract: 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.