RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Uspekhi Mat. Nauk: Year: Volume: Issue: Page: Find

 Uspekhi Mat. Nauk, 1987, Volume 42, Issue 6(258), Pages 25–60 (Mi umn2653)

On the determination of minimal global attractors for the Navier–Stokes and other partial differential equations

Full text: PDF file (2567 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1987, 42:6, 27–73

Bibliographic databases:

UDC: 517.9
MSC: 76D05, 35Q30, 35B41, 37B25, 35K20, 35L20

Citation: O. A. Ladyzhenskaya, “On the determination of minimal global attractors for the Navier–Stokes and other partial differential equations”, Uspekhi Mat. Nauk, 42:6(258) (1987), 25–60; Russian Math. Surveys, 42:6 (1987), 27–73

Citation in format AMSBIB
\Bibitem{Lad87} \by O.~A.~Ladyzhenskaya \paper On~the determination of minimal global attractors for the Navier--Stokes and other partial differential equations \jour Uspekhi Mat. Nauk \yr 1987 \vol 42 \issue 6(258) \pages 25--60 \mathnet{http://mi.mathnet.ru/umn2653} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=933994} \zmath{https://zbmath.org/?q=an:0687.35072} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1987RuMaS..42...27L} \transl \jour Russian Math. Surveys \yr 1987 \vol 42 \issue 6 \pages 27--73 \crossref{https://doi.org/10.1070/RM1987v042n06ABEH001503} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987Q195200002} 

• http://mi.mathnet.ru/eng/umn2653
• http://mi.mathnet.ru/eng/umn/v42/i6/p25

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. V. Babin, M. I. Vishik, “Spectral and stabilized asymptotic behaviour of solutions of non-linear evolution equations”, Russian Math. Surveys, 43:5 (1988), 121–164
2. I. D. Chueshov, “The strong solutions and the attractor of Karman equations system”, Math. USSR-Sb., 69:1 (1991), 25–36
3. A. A. Ilyin, “The Navier–Stokes and Euler equations on two-dimensional closed manifolds”, Math. USSR-Sb., 69:2 (1991), 559–579
4. O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89
5. A. V. Babin, “Asymptotics as $|x|\to\infty$ of functions lying on an attractor of the two-dimensional Navier–Stokes system in an unbounded plane domian”, Math. USSR-Sb., 74:2 (1993), 427–453
6. S. A. Vakulenko, “Existence of chemical waves with a complex motion of the front”, U.S.S.R. Comput. Math. Math. Phys., 31:5 (1991), 68–76
7. Tepper L. Gill, W. W. Zachary, “Dimensionality of Invariant Sets for Nonautonomous Processes”, SIAM J Math Anal, 23:5 (1992), 1204
8. Don A Jones, Edriss S Titi, “On the number of determining nodes for the 2D Navier–Stokes equations”, Journal of Mathematical Analysis and Applications, 168:1 (1992), 72
9. A. V. Romanov, “Sharp estimates of the dimension of inertial manifolds for nonlinear parabolic equations”, Russian Acad. Sci. Izv. Math., 43:1 (1994), 31–47
10. I. D. Chueshov, “Global attractors for non-linear problems of mathematical physics”, Russian Math. Surveys, 48:3 (1993), 133–161
11. A. A. Ilyin, “Partly dissipative semigroups generated by the Navier–Stokes system on two-dimensional manifolds, and their attractors”, Russian Acad. Sci. Sb. Math., 78:1 (1994), 47–76
12. A. V. Razgulin, “Self-excited oscillations in the nonlinear parabolic problem with transformed argument”, Comput. Math. Math. Phys., 33:1 (1993), 61–70
13. Wei Lin, Yi Zhao, “The global attractor of infinite—dimensional dynamical systems governed by a class of nonlinear parabolic variational inequalities and associated control problems”, Applicable Analysis, 54:3-4 (1994), 163
14. T. V. Girya, I. D. Chueshov, “Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems”, Sb. Math., 186:1 (1995), 29–45
15. V. S. Klimov, “Evolution problems in the mechanics of visco-plastic media”, Izv. Math., 59:1 (1995), 141–157
16. Lev Kapitanski, “Minimal compact global attractor for a damped semilinear wave equation”, Communications in Partial Differential Equations, 20:7-8 (1995), 1303
17. Tatsuo Yanagita, Kunihiko Kaneko, “Rayleigh-Bénard convection patterns, chaos, spatiotemporal chaos and turbulence”, Physica D: Nonlinear Phenomena, 82:3 (1995), 288
18. A. A. Ilyin, “Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides”, Sb. Math., 187:5 (1996), 635–677
19. N. M. Bessonov, S. A. Vakulenko, “Connected kink states in nonlinear inhomogeneous media”, Theoret. and Math. Phys., 107:1 (1996), 511–522
20. V. N. Starovoitov, “The dynamics of a two-component fluid in the presence of capillary forces”, Math. Notes, 62:2 (1997), 244–254
21. L. Boutet de Monvel, I.D. Chueshov, A.V. Rezounenko, “Long—time behaviour of strong solutions of retarded nonlinear P.D.E.s”, Communications in Partial Differential Equations, 22:9-10 (1997), 1453
22. I. D. Chueshov, “Theory of functionals that uniquely determine the asymptotic dynamics of infinite-dimensional dissipative systems”, Russian Math. Surveys, 53:4 (1998), 731–776
23. D. N. Cheban, “Bounded solutions of linear almost periodic differential equations”, Izv. Math., 62:3 (1998), 581–600
24. V. S. Klimov, “Topological characteristics of non-smooth functionals”, Izv. Math., 62:5 (1998), 969–984
25. V. S. Mel'nik, “Estimates of the fractal and Hausdorff dimensions of sets invariant under multimappings”, Math. Notes, 63:2 (1998), 190–196
26. I. D. Chueshov, “A remark on sets of determining elements for reaction-diffusion systems”, Math. Notes, 63:5 (1998), 679–687
27. L. S. Pankratov, I. D. Chueshov, “Homogenization of attractors of non-linear hyperbolic equations with asymptotically degenerate coefficients”, Sb. Math., 190:9 (1999), 1325–1352
28. A.O. Çelebi, V.K. Kalantarov, M. Polat, “Attractors for the Generalized Benjamin–Bona–Mahony Equation”, Journal of Differential Equations, 157:2 (1999), 439
29. I. N. Kostin, “An attractor for a semilinear wave equation with boundary damping”, Journal of Mathematical Sciences (New York), 98:6 (2000), 753
30. I. D. Chueshov, “Analyticity of global attractors and determining nodes for a class of damped non-linear wave equations”, Sb. Math., 191:10 (2000), 1541–1559
31. David I Santiago, Alexander S Silbergleit, “Global dynamics of cosmological expansion with a minimally coupled scalar field”, Physics Letters A, 268:1-2 (2000), 69
32. V. S. Klimov, “Infinite-dimensional version of the Poincare–Hopf theorem and homological characteristics of functionals”, Sb. Math., 192:1 (2001), 49–64
33. A. A. Kornev, “Approximation of attractors of semidynamical systems”, Sb. Math., 192:10 (2001), 1435–1450
34. A. V. Romanov, “Finite-dimensional dynamics on attractors of non-linear parabolic equations”, Izv. Math., 65:5 (2001), 977–1001
35. A. K. Abramyan, S. A. Vakulenko, “Dissipative and Hamiltonian Systems with Chaotic Behavior: An Analytic Approach”, Theoret. and Math. Phys., 130:2 (2002), 245–255
36. G. A. Seregin, N. N. Ural'tseva, “Ol'ga Aleksandrovna Ladyzhenskaya (on her 80th birthday)”, Russian Math. Surveys, 58:2 (2003), 395–425
37. M. I. Vishik, V. V. Chepyzhov, “Kolmogorov $\varepsilon$-Entropy in Problems on Global Attractors of Evolution Equations of Mathematical Physics”, Problems Inform. Transmission, 39:1 (2003), 2–20
38. A. A. Kornev, “On an iterative method for the construction the Hadamard mustaches”, Comput. Math. Math. Phys., 44:8 (2004), 1274–1283
39. E. L. Aero, S. A. Vakulenko, “Asymptotic Behavior of Solutions of a Strongly Nonlinear Model of a Crystal Lattice”, Theoret. and Math. Phys., 143:3 (2005), 782–791
40. Jack K. Hale, “Dissipation and Compact Attractors”, J Dyn Diff Equat, 18:3 (2006), 485
41. A. V. Romanov, “Effective finite parametrization in phase spaces of parabolic equations”, Izv. Math., 70:5 (2006), 1015–1029
42. A. A. Kornev, “A Method of Graph Transformation Type for Numerical Simulation of Invariant Manifolds”, Proc. Steklov Inst. Math., 256 (2007), 223–237
43. M. Yu. Kokurin, “Approximation of solutions to nonregular nonlinear equations by attractors of dynamic systems in a Banach space”, Russian Math. (Iz. VUZ), 51:1 (2007), 19–29
44. Claudio Giorgi, Vittorino Pata, Elena Vuk, “On the extensible viscoelastic beam”, Nonlinearity, 21:4 (2008), 713
45. A. K. Abramyan, S. A. Vakulenko, “Nonlinear Ritz method and the motion of defects”, Theoret. and Math. Phys., 155:2 (2008), 678–688
46. V. S. Klimov, “Topological characteristics of multi-valued maps and Lipschitzian functionals”, Izv. Math., 72:4 (2008), 717–739
47. Vittorino Pata, “Gradient systems of closed operators”, centr eur j math, 7:3 (2009), 487
48. M. Polat, A. O. Celebı, N. Cali⋅kan, “Global attractors for the 3D viscous Cahn-Hillard equations in an unbounded domain”, Gapa, 88:8 (2009), 1157
49. A. O. Celebı, V. K. Kalantarov, M. Polat, “Global attractors for 2D Navier–Stokes-Voight equations in an unbounded domain”, Gapa, 88:3 (2009), 381
50. C. Giorgi, M.G. Naso, V. Pata, M. Potomkin, “Global attractors for the extensible thermoelastic beam system”, Journal of Differential Equations, 246:9 (2009), 3496
51. Jack K. Hale, Geneviève Raugel, “A Modified Poincaré Method for the Persistence of Periodic Orbits and Applications”, J Dyn Diff Equat, 2010
52. S. A. Vakulenko, M. V. Cherkai, “Destruction of dissipative structures under random actions”, Theoret. and Math. Phys., 165:1 (2010), 1387–1399
53. M. I. Vishik, V. V. Chepyzhov, “Trajectory attractors of equations of mathematical physics”, Russian Math. Surveys, 66:4 (2011), 637–731
54. A. V. Babin, M. I. Vishik, “Attractors of partial differential evolution equations in an unbounded domain”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 116:3-4 (2011), 221
55. Pelin G. Geredeli, Azer Khanmamedov, “Long-time dynamics of the parabolic $p$-Laplacian equation”, CPAA, 12:2 (2012), 735
56. Vittorino Pata, Filippo Dell'Oro, “Memory relaxation of type III thermoelastic extensible beams and Berger plates”, EECT, 1:2 (2012), 251
57. Leonov G.A., “Funktsii lyapunova v teorii razmernosti attraktorov”, Prikladnaya matematika i mekhanika, 76:2 (2012), 180–196
58. V. V. Chepyzhov, “Uniform attractors of dynamical processes and non-autonomous equations of mathematical physics”, Russian Math. Surveys, 68:2 (2013), 349–382
59. V.G.. Zvyagin, S.K.. Kondratyev, “Approximating topological approach to the existence of attractors in fluid mechanics”, J. Fixed Point Theory Appl, 2013
60. M. S. Poltinnikova, “Formula for the Lyapunov Dimension for Two Connected Mappings of a Circle”, J Math Sci, 2013
61. V. S. Klimov, “Variational inequalities with strong nonlinearities”, Russian Math. (Iz. VUZ), 58:9 (2014), 22–35
62. V. G. Zvyagin, S. K. Kondrat'ev, “Attractors of equations of non-Newtonian fluid dynamics”, Russian Math. Surveys, 69:5 (2014), 845–913
63. Cheban D., “Belitskii-Lyubich Conjecture For C-Analytic Dynamical Systems”, Discrete Contin. Dyn. Syst.-Ser. B, 20:3, SI (2015), 945–959
64. A. B. Aliyev, S. E. Isayeva, “A global attractor for one semilinear hyperbolic equation with memory operator”, Comput. Math. Math. Phys., 55:11 (2015), 1823–1835
65. Zvyagin V., “Attractors Theory For Autonomous Systems of Hydrodynamics and Its Application to Bingham Model of Fluid Motion”, Lobachevskii J. Math., 38:4, SI (2017), 767–777
66. Bilgin B. Kalantarov V., “Determining Functionals For Damped Nonlinear Wave Equations”, Complex Var. Elliptic Equ., 63:7-8, SI (2018), 931–944
•  Number of views: This page: 1521 Full text: 355 References: 60 First page: 1