中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程研讨班
Speaker: 金锐（上海交通大学）
Inviter: Quoc-Hung Nguyen
Language: English
Title: Flexibility for the SQG Equation with an L⁴/³⁺ Active Scalar
Time & Venue：2026年9月1日（星期二）16:00-17:00 Meeting ID: 373 227 3489 Passcode: PDE2026
Abstract: We develop a new convex-integration scheme, building on the work of Bruè, Colombo, and Kumar (2026), for the inviscid surface quasi-geostrophic equation on the two-dimensional torus. For p=4/3+10⁻⁵, we prove a flexibility theorem for weak solutions in the standard momentum formulation with active scalar θ∈C([0,1];Lᵖ). The perturbations are constructed from localized, concentrated traveling SQG profiles whose centers move along rational directions and whose radii depend on the Reynolds stress. Time averages of auxiliary sources along these trajectories reconstruct the preceding-stage stress, while a two-dimensional bilinear null-form estimate compensates for the derivative loss caused by the nonlocal constitutive law. Exploiting the time-locality of the iteration, we also obtain a dense subset of the mean-zero space Lᵖ such that every initial datum in this subset admits nonuniqueness of weak solutions.
附件：