Work

Non-uniqueness of weak solutions for a logarithmically supercritical hyperdissipative Navier-Stokes system

Year: 2025

Type: article

Abstract: Existence of non-unique solutions of finite kinetic energy for the three dimensional Navier-Stokes equations is proved in the slightly supercritical hyper-dissipative setting introduced by Tao [20] . The result is based on the convex integration techniques of Buckmaster and Vicol [3] , and extends Luo and Titi [16] in the slightly supercritical setting. To reach the threshold identified by Tao, we introduce the impulsed Beltrami flows , a variant of the intermittent Beltrami flows of Buckmaster and Vicol.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.110989

Authors: Marco Romito, Francesco Triggiano

Institutions: University of Pisa, Scuola Normale Superiore

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funders: European Commission, Università di Pisa, Ministero dell'Istruzione e del Merito