Onsager critical solutions of the forced Navier-Stokes equations

2022/12/16 by Bruè, Elia, Colombo, Maria, Crippa, Gianluca +2 · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.08413

Abstract

We answer positively to [BDL22, Question 2.4] by building new examples of solutions to the forced 3d-Navier-Stokes equations with vanishing viscosity, which exhibit anomalous dissipation and which enjoy uniform bounds in the space L_t³ C_x^{1/3 - ε}, for any fixed ε >0. Our construction combines ideas of [BDL22] and [CCS22].

Cited by

• Dissipation concentration in two-dimensional fluids
• Exponentially mixing flows with slow enhanced dissipation

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