Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field

Flandoli F, Hofmanová M, Luo D, Nilssen T (2022)
Annals of Applied Probability 32(4): 2568-2586.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Flandoli, Franco; Hofmanová, MartinaUniBi; Luo, Dejun; Nilssen, Torstein
Abstract / Bemerkung
We are concerned with the problem of global well-posedness of the 3D Navier-Stokes equations on the torus with unitary viscosity. While a full answer to this question seems to be out of reach of the current techniques, we establish a regularization by a deterministic vector field. More precisely, we consider the vorticity form of the system perturbed by an additional transport type term. Such a perturbation conserves the enstrophy and therefore a priori it does not imply any smoothing. Our main result is a construction of a deterministic vector field v = v(t, x) which provides the desired regularization of the system and yields global well-posedness for large initial data outside arbitrary small sets. The proof relies on probabilistic arguments developed by Flandoli and Luo, tools from rough path theory by Hofmanova, Leahy and Nilssen and a new Wong-Zakai approximation result, which itself combines probabilistic and rough path techniques.
Stichworte
3D Navier-Stokes equations; vorticity form; well-posedness; regularization by noise; Wong-Zakai principle
Erscheinungsjahr
2022
Zeitschriftentitel
Annals of Applied Probability
Band
32
Ausgabe
4
Seite(n)
2568-2586
ISSN
1050-5164
Page URI
https://pub.uni-bielefeld.de/record/2965535

Zitieren

Flandoli F, Hofmanová M, Luo D, Nilssen T. Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field . Annals of Applied Probability. 2022;32(4):2568-2586.
Flandoli, F., Hofmanová, M., Luo, D., & Nilssen, T. (2022). Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field . Annals of Applied Probability, 32(4), 2568-2586. https://doi.org/10.1214/21-AAP1740
Flandoli, Franco, Hofmanová, Martina, Luo, Dejun, and Nilssen, Torstein. 2022. “ Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field ”. Annals of Applied Probability 32 (4): 2568-2586.
Flandoli, F., Hofmanová, M., Luo, D., and Nilssen, T. (2022). Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field . Annals of Applied Probability 32, 2568-2586.
Flandoli, F., et al., 2022. Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field . Annals of Applied Probability, 32(4), p 2568-2586.
F. Flandoli, et al., “ Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field ”, Annals of Applied Probability, vol. 32, 2022, pp. 2568-2586.
Flandoli, F., Hofmanová, M., Luo, D., Nilssen, T.: Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field . Annals of Applied Probability. 32, 2568-2586 (2022).
Flandoli, Franco, Hofmanová, Martina, Luo, Dejun, and Nilssen, Torstein. “ Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field ”. Annals of Applied Probability 32.4 (2022): 2568-2586.
Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®
Suchen in

Google Scholar