Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations
Rehmeier M, Schenke A (2023)
Nonlinear Analysis : Theory, Methods & Applications 227: 113179.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Einrichtung
Abstract / Bemerkung
We study the incompressible hypodissipative Navier-Stokes equations with dis-sipation exponent 0 < alpha < 21 on the three-dimensional torus perturbed by an additive Wiener noise term and prove the existence of an initial condition for which distinct probabilistic weak solutions exist. To this end, we employ convex integration methods to construct a pathwise probabilistically strong solution, which violates a pathwise energy inequality up to a suitable stopping time. This paper seems to be the first in which such solutions are constructed via Beltrami waves instead of intermittent jets or flows in a stochastic setting.(c) 2022 Elsevier Ltd. All rights reserved.
Stichworte
Stochastic partial differential equations;
Fractional Navier-Stokes;
equations;
Convex integration;
Nonuniqueness;
Martingale solutions
Erscheinungsjahr
2023
Zeitschriftentitel
Nonlinear Analysis : Theory, Methods & Applications
Band
227
Art.-Nr.
113179
ISSN
0362-546X
eISSN
1873-5215
Page URI
https://pub.uni-bielefeld.de/record/2969178
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Rehmeier M, Schenke A. Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations. Nonlinear Analysis : Theory, Methods & Applications . 2023;227: 113179.
Rehmeier, M., & Schenke, A. (2023). Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations. Nonlinear Analysis : Theory, Methods & Applications , 227, 113179. https://doi.org/10.1016/j.na.2022.113179
Rehmeier, Marco, and Schenke, Andre. 2023. “Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations”. Nonlinear Analysis : Theory, Methods & Applications 227: 113179.
Rehmeier, M., and Schenke, A. (2023). Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations. Nonlinear Analysis : Theory, Methods & Applications 227:113179.
Rehmeier, M., & Schenke, A., 2023. Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations. Nonlinear Analysis : Theory, Methods & Applications , 227: 113179.
M. Rehmeier and A. Schenke, “Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations”, Nonlinear Analysis : Theory, Methods & Applications , vol. 227, 2023, : 113179.
Rehmeier, M., Schenke, A.: Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations. Nonlinear Analysis : Theory, Methods & Applications . 227, : 113179 (2023).
Rehmeier, Marco, and Schenke, Andre. “Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations”. Nonlinear Analysis : Theory, Methods & Applications 227 (2023): 113179.
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