Speaker: 寿凌云副教授，南京师范大学

Inviter: 杨明轩

Title: Optimal Decay, Gevrey Analyticity, and Low-Frequency Regularity for Viscous Compressible Fluids with Capillarity

Language: Chinese

Time & Venue: 2026.08.14 10:00-11:00 腾讯会议：869-584-100

Abstract: We study the Cauchy problem for the multi-dimensional Navier--Stokes equations of viscous compressible fluids with capillarity. A key point in the capillary model is its hidden diffusion mechanism: due to the coupling between viscosity and capillarity, the density fluctuation acquires a heat-like diffusive behavior. This enables us to establish an equivalent connection between optimal decay, Gevrey analyticity, and low-frequency regularity. For given global solutions, we prove that the boundedness of the low-frequency part of the initial perturbation in a Besov space with negative regularity exponent is not only sufficient but also necessary for obtaining Gevrey analyticity and upper decay bounds for arbitrary higher-order derivatives. We further establish a sharp two-sided decay characterization: the matching upper and lower decay bounds hold if and only if the low-frequency initial data belong to a suitable nondegenerate subset of this Besov space. The proof combines a refined low-frequency spectral analysis, inspired in part by the work of Hoff and Zumbrun, with nonlinear estimates that track the growth of the analyticity radius and quantify the faster decay of the discrepancy between the nonlinear solution and the associated diffusion profile.