Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions

Munteanu I, Röckner M (2019)
JOURNAL OF EVOLUTION EQUATIONS.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck| Englisch
 
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Autor*in
Munteanu, Ionut; Röckner, MichaelUniBi
Abstract / Bemerkung
The aim of this work is to prove an existence and uniqueness result of Kato-Fujita type for the Navier-Stokes equations, in vorticity form, in 2D and 3D, perturbed by a gradient-type multiplicative Gaussian noise (for sufficiently small initial vorticity). These equations are considered in order to model hydrodynamic turbulence. The approach was motivated by a recent result by Barbu and Rockner (J Differ Equ 263:5395-5411, 2017) that treats the stochastic 3D Navier-Stokes equations, in vorticity form, perturbed by linear multiplicative Gaussian noise. More precisely, the equation is transformed to a random nonlinear parabolic equation, as in Barbu and Rockner (2017), but the transformation is different and adapted to our gradient-type noise. Then, global unique existence results are proved for the transformed equation, while for the original stochastic Navier-Stokes equations, existence of a solution adapted to the Brownian filtration is obtained up to some stopping time.
Stichworte
Stochastic Navier-Stokes equation; Turbulence; Vorticity; Biot-Savart; operator; Gradient-type noise
Erscheinungsjahr
2019
Zeitschriftentitel
JOURNAL OF EVOLUTION EQUATIONS
ISSN
1424-3199
eISSN
1424-3202
Page URI
https://pub.uni-bielefeld.de/record/2939170

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Munteanu I, Röckner M. Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions. JOURNAL OF EVOLUTION EQUATIONS. 2019.
Munteanu, I., & Röckner, M. (2019). Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions. JOURNAL OF EVOLUTION EQUATIONS. doi:10.1007/s00028-019-00551-3
Munteanu, I., and Röckner, M. (2019). Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions. JOURNAL OF EVOLUTION EQUATIONS.
Munteanu, I., & Röckner, M., 2019. Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions. JOURNAL OF EVOLUTION EQUATIONS.
I. Munteanu and M. Röckner, “Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions”, JOURNAL OF EVOLUTION EQUATIONS, 2019.
Munteanu, I., Röckner, M.: Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions. JOURNAL OF EVOLUTION EQUATIONS. (2019).
Munteanu, Ionut, and Röckner, Michael. “Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions”. JOURNAL OF EVOLUTION EQUATIONS (2019).