Ergodicity for the Randomly Forced 2D Navier–Stokes Equations

By Sergei B. Kuksin, Armen Shirikyan. 2001

76 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/967ff2f24e526eeccd0d7e04f0d461c869fd9df6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Arnaud Debussche
2. Giuseppe Da Prato
3. A. Agrachev
4. Andrey V. Sarychev
5. Tomasz Komorowski
6. Tomasz Szarek
7. S. Peszat
8. Armen Shirikyan

In Finance

1. Arnaud Debussche
2. Giuseppe Da Prato
3. Tomasz Komorowski
4. Martin Hairer
5. S. Peszat
6. Armen Shirikyan
7. Sergei B. Kuksin
8. A. Agrachev

In Mathematical Physics

1. Arnaud Debussche
2. Giuseppe Da Prato
3. Sergei B. Kuksin
4. Armen Shirikyan
5. Tomasz Komorowski
6. A. Agrachev
7. Andrey V. Sarychev
8. S. Peszat

Citations in the corpus

• On ergodicity of some Markov processes (2008, methodology): “he process Z(t):=V(t,x(t)+·) is a solution of a certain evolution equation in a Hilbert space; see (5.5) below. With the help of the technique developed by Hairer and Mattingly [11] (see also [5] and [14]), we verify the assumptions of Theorem 3 when V(t,x) is periodic in the xvariable and satisfies ”
• Navier–Stokes Equations: Controllability by Means of Low Modes Forcing (2005, methodology): “Following [ 15 ] we call this method Lyapunov–Schmidt type reduction.”
• 2D Stochastic Navier–Stokes Equations with a Time-Periodic Forcing Term (2008, background): “Recently much progress has been obtained in the study of existence, uniqueness and ergodicity of the associated invariant measures ([3], [15], [17], [18], [19], [ 20 ], [21], [11], [22], [23]) when f(t) = 0. Also in the 3D case, there has been a lot of recent progress ([6], [9], [13], [16], [25], [2”
• An Introduction to 3D Stochastic Fluid Dynamics (2008, unknown): “The theory in the 2D case is richer of well posedness results, even for cylindrical noise, ergodicity, control, non-viscous case and limit, see among others references [2], [3], [4], [6], [8], [9], [11], [13], [14], [17], [21], [22], [23], [28], [30], [31], [32], [47], [ 49 ], [50], [51], [55], [56]”
• Ergodicity Results for the Stochastic Navier–Stokes Equations: An Introduction (2013, background): “Then, these arguments were generalized in several directions and the theory was extended to many other equations (see for instance [23], [35], [37], [43], [41], [44], [45] , [46], [56], [57], [63]).”
• A Coupling Approach¶to Randomly Forced Nonlinear PDE's. I (2001, methodology): “In [ KS3 ] the NS equations (0.5) with an unbounded kick-force η(t, x) is studied and the scheme of [KS1] is used to prove the uniqueness and ergodicity of a stationary measure.”