Calculus of Variations and Geometric Measure Theory

E. Bruè - M. Colombo - G. Crippa - C. De Lellis - M. Sorella

Onsager critical solutions of the forced Navier-Stokes equations

created by bruè on 25 Dec 2022
modified on 05 Jun 2023


Published Paper

Inserted: 25 dec 2022
Last Updated: 5 jun 2023

Journal: Communications on Pure and Applied Analysis
Year: 2022


We answer positively to BDL22, Question 2.4 by building new examples of solutions to the forced three-dimensional Navier-Stokes equations with vanishing viscosity, which exhibit anomalous dissipation and which enjoy uniform bounds in the space $L^3_t C^{\frac{1}{3}-\varepsilon}_x$, for any fixed $\varepsilon >0$. Our construction combines ideas of BDL22 and CCS22.