Onsager critical solutions of the forced Navier-Stokes equations

Elia Bruè; Maria Colombo; Gianluca Crippa; Camillo De Lellis; Massimo Sorella

Onsager critical solutions of the forced Navier-Stokes equations

Analysis of PDEs 2022-12-19 v1

Authors: Elia Bruè , Maria Colombo , Gianluca Crippa , Camillo De Lellis , Massimo Sorella

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 $L_t^3 C_x^{1/3 - \varepsilon}$ , for any fixed $\varepsilon >0$ . Our construction combines ideas of [BDL22] and [CCS22].

Keywords

forced navier-stokes equations anomalous dissipation onsager critical solutions vanishing viscosity uniform bounds three-dimensional flows

Cite

@article{arxiv.2212.08413,
  title  = {Onsager critical solutions of the forced Navier-Stokes equations},
  author = {Elia Bruè and Maria Colombo and Gianluca Crippa and Camillo De Lellis and Massimo Sorella},
  journal= {arXiv preprint arXiv:2212.08413},
  year   = {2022}
}

Comments

15 pages

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