Year: 2026
Type: preprint
Abstract: We consider the uniqueness of the solution of the dissipative surface quasi-geostrophic equation, without assuming time-continuity and smallness of the solutions. We show that the uniqueness holds in the scale-critical Lebesgue spaces and non-homogeneous Besov spaces. The proof is based on the energy method, inspired by the approach introduced by Lions and Masmoudi (2001) in the study of uniqueness for the Navier-Stokes equations. A key ingredient of the argument is the justification of the energy inequality via the smoothing effect of the fractional heat semigroup together with an iteration scheme based on the structure of the integral equation.
Source: arXiv (Cornell University)
Author: Okazaki, Taiki
Institution: Tohoku University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164600801