Global solutions to random 3D vorticity equations for small initial data

Barbu V, Röckner M (2017)
Journal of Differential Equations 263(9): 5395-5411.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Barbu, Viorel; Röckner, MichaelUniBi
Abstract / Bemerkung
One proves the existence and uniqueness in (L-P (R-3))(3), 3/2< p < 2, of a global mild solution to random vorticity equations associated to stochastic 3D Navier Stokes equations with linear multiplicative Gaussian noise of convolution type, for sufficiently small initial vorticity. This resembles some earlier deterministic results of T. Kato [16] and are obtained by treating the equation in vorticity form and reducing the latter to a random nonlinear parabolic equation. The solution has maximal regularity in the spatial variables and is weakly continuous in (L-3 boolean AND L (3p/4p-6))(3) with respect to the time variable. Furthermore, we obtain the pathwise continuous dependence of solutions with respect to the initial data. In particular, one gets a locally unique solution of 3D stochastic Navier Stokes equation in vorticity form up to some explosion stopping time r adapted to the Brownian motion. (C) 2017 Elsevier Inc. All rights reserved.
Stichworte
Stochastic Navier Stokes equation; Vorticity; Biot-Savart operator
Erscheinungsjahr
2017
Zeitschriftentitel
Journal of Differential Equations
Band
263
Ausgabe
9
Seite(n)
5395-5411
ISSN
0022-0396
eISSN
1090-2732
Page URI
https://pub.uni-bielefeld.de/record/2914407

Zitieren

Barbu V, Röckner M. Global solutions to random 3D vorticity equations for small initial data. Journal of Differential Equations. 2017;263(9):5395-5411.
Barbu, V., & Röckner, M. (2017). Global solutions to random 3D vorticity equations for small initial data. Journal of Differential Equations, 263(9), 5395-5411. doi:10.1016/j.jde.2017.06.020
Barbu, V., and Röckner, M. (2017). Global solutions to random 3D vorticity equations for small initial data. Journal of Differential Equations 263, 5395-5411.
Barbu, V., & Röckner, M., 2017. Global solutions to random 3D vorticity equations for small initial data. Journal of Differential Equations, 263(9), p 5395-5411.
V. Barbu and M. Röckner, “Global solutions to random 3D vorticity equations for small initial data”, Journal of Differential Equations, vol. 263, 2017, pp. 5395-5411.
Barbu, V., Röckner, M.: Global solutions to random 3D vorticity equations for small initial data. Journal of Differential Equations. 263, 5395-5411 (2017).
Barbu, Viorel, and Röckner, Michael. “Global solutions to random 3D vorticity equations for small initial data”. Journal of Differential Equations 263.9 (2017): 5395-5411.

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