On random measures on spaces of trajectories and strong and weak solutions of stochastic equations

2004 ◽  
Vol 56 (5) ◽  
pp. 753-763
Author(s):  
A. A. Dorogovtsev
Keyword(s):  
Weak Solutions ◽  
Stochastic Equations ◽  
Random Measures

On weak solutions of stochastic equations in Hilbert spaces

1994 ◽  
Vol 46 (1-2) ◽  
pp. 41-51 ◽  
Author(s):  
Dariusz Gątarek ◽  
Beniamin Gołdys
Keyword(s):  
Hilbert Spaces ◽  
Weak Solutions ◽  
Stochastic Equations

scholarly journals Attractors for the Stochastic 3D Navier–Stokes Equations

2003 ◽  
Vol 03 (03) ◽  
pp. 279-297 ◽  
Author(s):  
Pedro Marín-Rubio ◽  
James C. Robinson
Keyword(s):  
White Noise ◽  
Global Attractor ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Stochastic Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Additive White Noise ◽  
Solutions Of Equations

In a 1997 paper, Ball defined a generalised semiflow as a means to consider the solutions of equations without (or not known to possess) the property of uniqueness. In particular he used this to show that the 3D Navier–Stokes equations have a global attractor provided that all weak solutions are continuous from (0, ∞) into L2. In this paper we adapt his framework to treat stochastic equations: we introduce a notion of a stochastic generalised semiflow, and then show a similar result to Ball's concerning the attractor of the stochastic 3D Navier–Stokes equations with additive white noise.

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