Work

An Onsager-type theorem for SQG equations

Year: 2026

Type: article

Abstract: We construct non-trivial weak solutions \theta\in C_{t}^{0}C_{x}^{0-} to the surface quasi-geostrophic (SQG) equations, which have compact support in time and thus violate the conservation of the Hamiltonian. The result is sharp in view of the fact that such a conservation law holds for all weak solutions in the class C_{t,x}^{0} \subset L_{t,x}^{3} (Isett and Vicol (2015)) and resolves the Onsager conjecture for SQG equations. The construction is achieved by means of a Nash iteration together with the linear decoupling method recently introduced by Giri and Radu (2023).

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1812

Authors: Mimi Dai, Vikram Giri, Răzvan-Octavian Radu

Institutions: University of Illinois Chicago, ETH Zurich, Princeton University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7223098794

FWCI: 24.18

Cites: 8

Cited by: 17

Related to: 10