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

Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and... J. Evol. Equ. Journal of Evolution © 2019 Springer Nature Switzerland AG Equations https://doi.org/10.1007/s00028-019-00551-3 Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions Ionut ¸ Munteanu and Michael Röckner Abstract. 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 Röckner (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 Röckner (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. 1. Introduction One of the most important features concerning the Navier–Stokes equation is its relation to the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

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

Journal of Evolution Equations , Volume OnlineFirst – Nov 9, 2019

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References (18)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-019-00551-3
Publisher site
See Article on Publisher Site

Abstract

J. Evol. Equ. Journal of Evolution © 2019 Springer Nature Switzerland AG Equations https://doi.org/10.1007/s00028-019-00551-3 Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions Ionut ¸ Munteanu and Michael Röckner Abstract. 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 Röckner (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 Röckner (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. 1. Introduction One of the most important features concerning the Navier–Stokes equation is its relation to the

Journal

Journal of Evolution EquationsSpringer Journals

Published: Nov 9, 2019

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