Book - Livre
S. Kuksin, A. Shirikyan. Mathematics of Two-Dimensional Turbulence, Cambridge University Press, Cambridge, 2012.

 
Papers in reviewed journals - Articles dans des revues à comité de lecture 

1. A. R. Shirikyan. On classical almost periodic solutions of nonlinear  hyperbolic equations, Math. Notes 54 (1993), no. 6, 1288-1290.

2. A. R. Shirikyan. On almost periodic solutions of nonlinear hyperbolic equations, Moscow  Univ. Math. Bull. 49 (1994), no. 5, 5-8.

3. A. R. Shirikyan. Almost periodic solutions  to  nonlinear  hyperbolic  equations, Moscow  Univ. Math. Bull. 49 (1994), no. 6, 4-7.

4. L. R. Volevich, A. R. Shirikyan. Quasilinear hyperbolic  equations. Solutions bounded in time and almost periodic in time, Russian J. Math. Phys. 4 (1996),  no. 4, 527-538.

5. L. R. Volevich, A. R. Shirikyan. Bounded and almost periodic in time  solutions to nonlinear high-order hyperbolic  equations, Trans. Moscow Math. Soc. 58 (1997), 89-135.

6. L. R. Volevich, A. R. Shirikyan. Exponential dichotomy and exponential splitting for hyperbolic equations, Trans. Moscow Math. Soc. 59 (1998), 95-133.

7. A. Shirikyan, L. Volevich. Bounded and almost periodic solutions  to linear high-order hyperbolic  equations, Math. Nachr. 193 (1998), 137-197. PS  PDF

8. A. Shirikyan.  Asymptotic behaviour of solutions to second-order hyperbolic equations with a nonlinear damping term, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. XXII (1998), no. 1, 1-21.

9. L. R. Volevich, A. R. Shirikyan. Stable and unstable manifolds for nonlinear elliptic equations  with parameter, Trans. Moscow Math. Soc. 61 (2000), 97-138.

10. L. R. Volevich, A. R. Shirikyan. Local dynamics for high-order semilinear hyperbolic equations,  Izv. Math. 64 (2000), no. 3, 439-485.  PS  PDF

11. S. Kuksin, A. Shirikyan. Stochastic dissipative PDE's and Gibbs measures,  Comm. Math. Phys. 213 (2000), no. 2, 291-330. PS   PDF

12. S. Kuksin, A. Shirikyan. Ergodicity for the randomly forced 2D Navier-Stokes equations, Math. Phys. Anal. Geom. 4 (2001), no. 2, 147-195.  PS   PDF

13. S. Kuksin, A. Shirikyan. A coupling approach to randomly forced nonlinear PDE's. I, Comm. Math. Phys. 221 (2001), no. 2, 351-366. PS   PDF

14. S. Kuksin, A. Piatnitsky, A. Shirikyan. A coupling approach to randomly forced nonlinear PDE's. II, Comm. Math. Phys. 230 (2002), no. 1, 81-85. PS  PDF

15. S. Kuksin, A. Shirikyan. On dissipative systems perturbed by bounded random kick-forces, Ergodic Theory Dynam. Systems 22 (2002), 1487-1495. PS   PDF

16. A. Shirikyan, L. Volevich. Exponential dichotomy and time-bounded solutions for first-order hyperbolic systems, J. Dynam. Differential Equations 14 (2002), no. 4, 777-827. PS   PDF

17. A. Shirikyan. Analyticity of solutions for randomly forced two-dimensional Navier-Stokes equations, Russian Math. Surveys 57 (2002), no. 4, 785-799. PS   PDF

18. S. Kuksin, A. Shirikyan. Coupling approach to white-forced nonlinear PDE's, J. Math. Pures Appl. 81 (2002), no. 6, 567-602. PS   PDF

19. S. Kuksin, A. Shirikyan. Some limiting properties of randomly forced 2D Navier-Stokes equations, Proc. Roy. Soc. Edinburgh Sect. A, 133 (2003), no. 4, 875-891. PS   PDF

20. S. Kuksin, A. Shirikyan. On random attractors for mixing-type systems, Funct. Anal. Appl., 38 (2004), no. 1, 34-46. PS   PDF

21. A. Shirikyan, L. Volevich. Qualitative properties of solutions for linear and non-linear hyperbolic PDE's, Discrete Contin. Dynam. Systems, Series A 10 (2004), no. 1-2, 517-542. PS   PDF

22. A. Shirikyan. Exponential mixing for 2D Navier-Stokes equations perturbed by an unbounded noise,  J. Math. Fluid Mech. 6 (2004), no. 2, 169-193. PS   PDF

23.  S. Kuksin, A. Shirikyan. Randomly forced CGL equation: stationary measures and the inviscid limit, Journal of Physics A: Mathematical and General 37 (2004), no. 12, 3805-3822. PS    PDF

24. A. Shirikyan. Ergodicity for a class of Markov processes and applications to randomly forced PDE's I,  Russian J. Math. Phys. 12 (2005), no. 1, 81-96. PS   PDF

25. A. Shirikyan. Law of large numbers and central limit theorem for randomly forced PDE's, Prob. Theory Related Fields 134 (2006), no. 2, 215-247. PS   PDF

26. A. Shirikyan. Ergodicity for a class of Markov processes and applications to randomly forced PDE's II,  Discrete Contin. Dynam. Systems 6 (2006), no. 4, 911-926. PS   PDF

27. A. Shirikyan. Approximate controllability for three-dimensional Navier-Stokes equations, Comm. Math. Phys. 266 (2006), no. 1, 123-151. PS    PDF

28. A. Agrachev, S. Kuksin, A. Sarychev, A. Shirikyan. On finite-dimensional projections of distributions for solutions of randomly forced PDE's, Annales de l'IHP 43 (2007), 399-415. PS   PDF

29. A. Shirikyan. Exact controllability in projections for three-dimensional Navier-Stokes equations, Annales de l'IHP, Analyse Non Linéaire 24 (2007), 521-537. PS   PDF

30. A. Shirikyan. Qualitative properties of stationary measures for three-dimensional Navier–Stokes equations, J. Funct. Anal. 249 (2007), 284-306. PDF

31. A. Shirikyan. Euler equations are not exactly controllable by a finite-dimensional external force, Physica D 237 (2008), no. 10-12, 1317-1323. PDF

32. A. Shirikyan. Local times for solutions of the complex Ginzburg-Landau equation and the inviscid limit, J. Math. Anal. Appl. 384 (2011), 130-137. PDF

33. V. Barbu, S. Rodrigues, A. Shirikyan. Internal exponential stabilization to a non-stationary solution for 3D Navier-Stokes equations, SIAM Journal Control Optimization 49 (2011), no. 4, 1454-1478. PDF

34. E. Priola, A. Shirikyan, L. Xu, J. Zabczyk, Exponential ergodicity and regularity for equations with Lévy noise, Stochastic Process. Appl. 122 (2012), no. 1, 106-133.  PDF

35. A. Shirikyan, S. Zelik. Exponential attractors for random dynamical systems and applications, Stochastic PDEs 1 (2013), no 2, 241–281. PDF

36. A. Shirikyan. Control and mixing for 2D Navier-Stokes equations with space-time localised noise,  Ann. Sci. Éc. Norm. Supér. 48 (2015), no. 2, 253–280. PDF

37. V. Jaksic, V. Nersesyan, C.-A. Pillet, A. Shirikyan. Large deviations from a stationary measure for a class of dissipative PDEs with random kicks, Comm. Pure Appl. Math. 68 (2015), no. 12, 2108-2143. PDF 

38. V. Jaksic, V. Nersesyan, C.-A. Pillet, A. Shirikyan. Large deviations and Gallavotti–Cohen principle for dissipative PDEs with rough noise, Comm. Math. Phys. 336 (2015), no. 1, 131–170. PDF

39. K. Ammari, T. Duyckaerts, A. Shirikyan. Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation, Math. Control Relat. Fields  6 (2016), no. 1, 1-25 PDF

40. V. Jaksic, C.-A. Pillet, A. Shirikyan. Entropic fluctuations in Gaussian dynamical systems, Rep. Math. Phys. 77 (2016), no. 3, 335–376. PDF 

41. V. Jaksic, C.-A. Pillet, A. Shirikyan. Entropic fluctuations in thermally driven harmonic networks, J. Stat. Phys. 166 (2017), no. 3-4, 926–1015. PDF 

42. A. Shirikyan. Global exponential stabilisation for the Burgers equation with localised control, J. Éc. polytech. Math. 4 (2017), 613–632. PDF 

43. S. Kuksin, A. Shirikyan. Rigorous results in space-periodic two-dimensional turbulence, Physics of Fluids 29 (2017), 125106. PDF

44. A. Shirikyan. Controllability implies mixing. I. Convergence in the total variation metric, Russian Mathematical Surveys 72 (2017), no. 5,939–953. PDF 

45. A. Shirikyan. Control theory for the Burgers equation: Agrachev-Sarychev approach,  Pure Appl. Funct. Anal. 3 (2018), no. 1, 219–240. PDF

46. V. Jaksic, V. Nersesyan, C.-A. Pillet, A. Shirikyan. Large deviations and mixing for dissipative PDEs with unbounded random kicks, Nonlinearity  31 (2018), no. 2, 540–596. PDF 

47. N. Cuneo, V. Jaksic, C.-A. Pillet, A. Shirikyan. Large deviations and fluctuation theorem for selectively decoupled measures on shift spaces,  Rev. Math. Phys. 31 (2019), no. 10, 1950036, 54 pp. PDF 

48. S. Kuksin, V. Nersesyan, A. Shirikyan. Exponential mixing for a class of dissipative PDEs with bounded degenerate noise,  Geom. Funct. Anal. 30 (2020), no. 1, 126–187. PDF 

49. S. Kuksin, V. Nersesyan, A. Shirikyan. Mixing via controllability for randomly forced nonlinear dissipative PDEs,  J. Éc. polytech. Math. 7 (2020), 871–896. PDF

50. A. Shirikyan. Controllability implies mixing II. Convergence in the dual-Lipschitz metric, Journal of the European Mathematical Society J. Eur. Math. Soc. (JEMS) 23 (2021), no. 4, 1381–1422. PDF 

51. V. Jaksic, V. Nersesyan, C.-A. Pillet, A. Shirikyan. Large deviations and entropy production in viscous fluid flows, Arch. Ration. Mech. Anal. 240 (2021), no. 3, 1675–1725. PDF 

52. J. Foldes, A. Shirikyan. Rayleigh-Bénard convection with stochastic forcing localised near the bottom, Preprint. PDF 

53. A. Djurdjevac, A. Shirikyan. Exponential stability of the flow for a generalised Burgers equation on a circle, Preprint. PDF 

Publications in reviewed proceedings of conferences - Conférences publiées avec comité de lecture 

1. A. R. Shirikyan. Almost periodic solutions of a non-linear hyperbolic  equation, Russian Math. Surveys 48 (1993), no. 4, 211-212.

2. A. R. Shirikyan. Asymptotic behaviour of solutions to the wave equation with a nonlinear damping term, Russian Math. Surveys 50 (1995), no.4, 809.

3. L. R. Volevich, A. R. Shirikyan. Bounded and almost periodic in time solutions for strongly nonlinear hyperbolic equations, Russian Math. Surveys 51 (1996), no. 5, 984.

4. L. R. Volevich, A. R. Shirikyan. Local linearization for semilinear hyperbolic equations of high order, Russian Math. Surveys 53 (1998), no. 4, 827-828.

5. L. R. Volevich, A. R. Shirikyan. On infinite-dimensional dynamic systems generated by nonlinear hyperbolic equations, ZAMM, Z. Angew. Math. Mech. 78 (1998), Suppl. 3, S1073-S1074.

6. L. R. Volevich, A. R. Shirikyan. Asymptotic properties of solutions to high-order hyperbolic equations generalizing the damped wave equation, International Series in Numerical Mathematics 130 (1999), Birkhäuser-Verlag, Basel/Switzerland, 885-894.

7. L. R. Volevich, A. R. Shirikyan. A center manifold theorem for semilinear hyperbolic equations, ZAMM, Z. Angew. Math. Mech. 79 (1999), Suppl. 2, S313-S314.

8. L. R. Volevich, A. R. Shirikyan. Stable and unstable manifolds for nonlinear elliptic equations with parameter, ZAMM, Z. Angew. Math. Mech. 79 (1999), Suppl. 3, S805-S806. 

9. A. Shirikyan.  Analyticity of solutions and Kolmogorov's dissipation scale for 2D Navier-Stokes equations,  Evolution Equations: Propagation Phenomena - Global Existence - Influence of Non-Linearities, R. Picard, M. Reissig, W. Zajaczkowski (eds.),  Warszawa, 2003, 49-53. PS   PDF

10. A. Shirikyan. A version of the law of large numbers and applications, Probabilistic Methods in Fluids, Proceedings of the Swansea Workshop held on 14 - 19 April 2002, 263--271, World Scientific, New Jersey, 2003. PS   PDF

11. A. Shirikyan. Some mathematical problems of statistical hydrodynamics, XIV International Congress on Mathematical Physics, 304-311, World Sci. Publ., Hackensack, NJ, 2005. PS   PDF

12. A. Shirikyan. Controllability of three-dimensional Navier-Stokes equations and applications, Séminaire: Équations aux Dérivées Partielles, 2005-2006, École Polytechnique, Palaiseau, Exp. No. VI, 9 pp., 2006. PS   PDF

13. A. Shirikyan. Global controllability and mixing for the Burgers equation with localised finite-dimensional external force, New Trends in Differential Equations,  Control Theory and Optimization,  V. Barbu, C. Lefter, I. Vrabie (Eds),  pp. 293-300, 2016. PDF


Other publications - Autres publications 

1. L. R. Volevich, A. R. Shirikyan. Équations linéaires hyperboliques d'ordre supé rieur. Solutions bornées et presque-périodiques, C. R. Acad. Sci., Série I 324 (1997), no. 8, 879-884.

2. L. R. Volevich, A. R. Shirikyan. Some problems for strictly hyperbolic equations on the entire time-axis, Appendix in the Russian edition of the book: L. R. Volevich and S. G. Gindikin, Mixed Problems for Partial Differential Equations with Quasihomogeneous Principal Part, URSS, Moscow, 1999,  227-266.

3. A. Shirikyan. Controllability of nonlinear PDE's: Agrachev-Sarychev approach, Jounées EDP (2007), Exposé IV, 11 p.  PDF

4. A. Shirikyan. Exponential mixing for randomly forced partial differential equations: method of coupling, Instability in Models Connected with Fluid Flows. I, Edited by C. Bardos and A. Fursikov, International Mathematical Series, 6, Springer, 2008, 155-188. PDF

5. A. Shirikyan. Approximate controllability of the viscous Burgers equation on the real line, Geometric Control Theory and sub-Riemannian Geometry, G. Stefani, U. Boscain, J.-P. Gauthier, A. Sarychev, M. Sigalotti (Eds.), Springer INdAM Series, Vol. 5; 351–370, 2014. PDF

6. A. Shirikyan. Mixing for the Burgers Equation driven  by a localised two-dimensional stochastic forcing,  Evolution Equations, Long Time Behavior and Control, K. Ammari & S. Gerbi (Eds.), Cambridge, pp 179-194, 2017. PDF