On the stability of rarefaction for stochastic viscous conservation law

Speaker: 苏厚齐（首都师范大学）

Title: On the stability of rarefaction for stochastic viscous conservation law

Language: Chinese 

Time & Venue: 2026 年3月20日16:00–17:00 南楼613

Abstract: This talk investigates the asymptotic stability of rarefaction waves for stochastic viscous conservation laws driven by nonlinear conservative noise. This regime involves a critical scaling where stochastic fluctuations are of the same order as viscous dissipation. While kinetic and viscosity solution frameworks have been successful in other contexts, bridging the gap to the high-order regularity required for this specific stability analysis remains a challenge.} To address this, we develop a three-part approach \begin{enumerate} \item A {Stochastic Area Inequality} to control ccumulated energy fluctuations;  \item A {stochastic $\rm{L_{loc}^{1}}$ contraction principle} (via the Kružkov oubling-of-variables) to establish uniqueness for non-integrable profiles; \item A {modified Galerkin approximation} to preserve the {\rm{$H^2$}} energy structure.\end{enumerate}Our analysis first establishes a general rigidity result: provided the solution maintains regularity, it asymptotically converges to the rarefaction wave. Furthermore, we prove the global well-posedness for small initial perturbations. Notably, the critical competition between noise and dissipation suggests that this smallness condition reflects a physical threshold for stability rather than a purely technical limitation.