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- Sergei Kuksin, Armen Shirikyan
- 2000

We study a class of dissipative nonlinear PDEâ€™s forced by a random force Î·(t, x), with the space variable x varying in a bounded domain. The class contains the 2D Navierâ€“Stokes equations (underâ€¦ (More)

- Sergei Kuksin, Andrey L. Piatnitski, Armen Shirikyan
- 2005

We consider a class of discrete time random dynamical systems and establish the exponential convergence of its trajectories to a unique stationary measure. The result obtained applies, in particular,â€¦ (More)

- Sergei Kuksin, Armen Shirikyan
- 2002

We consider the 2D Navierâ€“Stokes system, perturbed by a white in time random force, such that sufficiently many of its Fourier modes are excited (e.g., all of them are). It is proved that the systemâ€¦ (More)

- Armen Shirikyan
- 2008

We show that the Euler system is not exactly controllable by a finitedimensional external force. The proof is based on the comparison of the Kolmogorov Îµ-entropy for HÃ¶lder spaces and for the classâ€¦ (More)

The paper is devoted to studying the problem of controllability for 3D Navierâ€“Stokes equations in a bounded domain. We develop the method introduced by Agrachev and Sarychev in the 2D case andâ€¦ (More)

- Armen Shirikyan
- 2005

The paper is devoted to studying controllability properties for 3D Navierâ€“Stokes equations in a bounded domain. We establish a sufficient condition under which the problem in question is exactlyâ€¦ (More)

- Armen Shirikyan
- 2007

We show that the Euler system is not exactly controllable by a finitedimensional external force. The proof is based on the comparison of the Kolmogorov Îµ-entropy for HÃ¶lder spaces and for the classâ€¦ (More)

- Viorel Barbu, SÃ©rgio S. Rodrigues, Armen Shirikyan
- SIAM J. Control and Optimization
- 2011

We consider the Navierâ€“Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control thatâ€¦ (More)

- Vojkan Jaksic, Vahagn Nersesyan, +5 authors Armen Shirikyan
- 2012

We study a class of dissipative PDEâ€™s perturbed by a bounded random kick force. It is assumed that the random force is non-degenerate, so that the Markov process obtained by the restriction ofâ€¦ (More)

- Armen Shirikyan
- 2004

The paper deals with infinite-dimensional random dynamical systems. Under the condition that the system in question is of mixing type and possesses a random compact attracting set, we show that theâ€¦ (More)