Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations

Fuente: arXiv
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Main Authors: Mengual, Francisco, Solera, Marcos
Format: Preprint
Published: 2026
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author Mengual, Francisco
Solera, Marcos
author_facet Mengual, Francisco
Solera, Marcos
contents We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique $\dot{H}^s$- 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_00331
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations
Mengual, Francisco
Solera, Marcos
Analysis of PDEs
Mathematical Physics
We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique $\dot{H}^s$- 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.
title Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations
topic Analysis of PDEs
Mathematical Physics
url https://arxiv.org/abs/2601.00331