Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations
Analysis of PDEs
2026-01-05 v1 Mathematical Physics
math.MP
Abstract
We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique - energy solutions below the Miura-Ju class. In particular, this shows that the solutions constructed by Resnick and Marchand for the dissipative SQG equation are not necessarily unique. Second, this establishes nonuniqueness below the Ladyzhenskaya-Prodi-Serrin class for the 2D Navier-Stokes equation, as well as below the Constantin-Wu and Dong-Chen-Zhao-Liu classes for the dissipative SQG equation.
Cite
@article{arxiv.2601.00331,
title = {Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations},
author = {Francisco Mengual and Marcos Solera},
journal= {arXiv preprint arXiv:2601.00331},
year = {2026}
}