On a rough perturbation of the Navier-Stokes system and its vorticity formulation

Hofmanová M, Leahy J-M, Nilssen T (2021)
Annals of Applied Probability 31(2): 736-777.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Hofmanová, MartinaUniBi; Leahy, James-Michael; Nilssen, Torstein
Abstract / Bemerkung
We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of strong solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Moreover, we derive rough path continuity of the equation, which yields a Wong-Zakai result for Brownian driving paths, and show that for a large class of driving signals, the system generates a continuous random dynamical system. In dimension three, the noise is not enstrophy balanced, and we establish the existence of local in time solutions.
Erscheinungsjahr
2021
Zeitschriftentitel
Annals of Applied Probability
Band
31
Ausgabe
2
Seite(n)
736-777
ISSN
1050-5164
Page URI
https://pub.uni-bielefeld.de/record/2937411

Zitieren

Hofmanová M, Leahy J-M, Nilssen T. On a rough perturbation of the Navier-Stokes system and its vorticity formulation. Annals of Applied Probability. 2021;31(2):736-777.
Hofmanová, M., Leahy, J. - M., & Nilssen, T. (2021). On a rough perturbation of the Navier-Stokes system and its vorticity formulation. Annals of Applied Probability, 31(2), 736-777. https://doi.org/10.1214/20-AAP1603
Hofmanová, M., Leahy, J. - M., and Nilssen, T. (2021). On a rough perturbation of the Navier-Stokes system and its vorticity formulation. Annals of Applied Probability 31, 736-777.
Hofmanová, M., Leahy, J.-M., & Nilssen, T., 2021. On a rough perturbation of the Navier-Stokes system and its vorticity formulation. Annals of Applied Probability, 31(2), p 736-777.
M. Hofmanová, J.-M. Leahy, and T. Nilssen, “On a rough perturbation of the Navier-Stokes system and its vorticity formulation”, Annals of Applied Probability, vol. 31, 2021, pp. 736-777.
Hofmanová, M., Leahy, J.-M., Nilssen, T.: On a rough perturbation of the Navier-Stokes system and its vorticity formulation. Annals of Applied Probability. 31, 736-777 (2021).
Hofmanová, Martina, Leahy, James-Michael, and Nilssen, Torstein. “On a rough perturbation of the Navier-Stokes system and its vorticity formulation”. Annals of Applied Probability 31.2 (2021): 736-777.
Link(s) zu Volltext(en)
Access Level
Restricted Closed Access

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Quellen

arXiv: 1902.09348

Suchen in

Google Scholar