@article{ASCFPA_1986__88_5_25_0,
author = {Biler, P.},
title = {Invariant sets of solutions of {Navier-Stokes} and related evolution equations - {A} survey},
journal = {Annales scientifiques de l'Universit\'e de Clermont-Ferrand 2. S\'erie Probabilit\'es et applications},
pages = {25--47},
year = {1986},
publisher = {UER de Sciences exactes et naturelles de l'Universit\'e de Clermont},
volume = {88},
number = {5},
mrnumber = {872120},
zbl = {0624.35069},
language = {en},
url = {https://www.numdam.org/item/ASCFPA_1986__88_5_25_0/}
}
TY - JOUR AU - Biler, P. TI - Invariant sets of solutions of Navier-Stokes and related evolution equations - A survey JO - Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications PY - 1986 SP - 25 EP - 47 VL - 88 IS - 5 PB - UER de Sciences exactes et naturelles de l'Université de Clermont UR - https://www.numdam.org/item/ASCFPA_1986__88_5_25_0/ LA - en ID - ASCFPA_1986__88_5_25_0 ER -
%0 Journal Article %A Biler, P. %T Invariant sets of solutions of Navier-Stokes and related evolution equations - A survey %J Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications %D 1986 %P 25-47 %V 88 %N 5 %I UER de Sciences exactes et naturelles de l'Université de Clermont %U https://www.numdam.org/item/ASCFPA_1986__88_5_25_0/ %G en %F ASCFPA_1986__88_5_25_0
Biler, P. Invariant sets of solutions of Navier-Stokes and related evolution equations - A survey. Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications, Tome 88 (1986) no. 5, pp. 25-47. https://www.numdam.org/item/ASCFPA_1986__88_5_25_0/
1 , , Attractor of the Navier-Stokes system and the parabolic equations and an estimate of their dimension, Zap. Nauch. Sem. LOMI, 115, 1982, 3-15. | Zbl | MR
2 -,,-, Attractors of the evolution partial differential equations and estimates of their dimension, Usp. Mat. Nauk, 38,4, 1983, 133-187. | Zbl | MR
3 -,,-, Regular attractors of semigroups and evolution equations, J. Math. pures appl. 62, 1983, 441-491. | Zbl | MR
4 -,,-, Estimates from above and below for the dimension of attractors of evolution equations, Sib.Mat. Zh. 24,5, 1983, 15-30.
5 -,,-, Attracteurs maximaux dans les equations aux dérivées partielles, Collège de France, Séminaire 1984, vol. VI, Pitman, Res.Notes in Math. and (in this volume ) A. Haraux, Two remarks on dissipative hyperbolic problems.
6 -,,-, Maximal attractors of semigroups corresponding to evolution differential equations, Mat. Sb. 126,3, 1985, 397-419. | Zbl | MR
7 , Attractors of evolution equations of nonlinear viscoelasticity, Vestnik MGU, 5, 1985, 69-71. | Zbl
8 , Large time behaviour of periodic solutions to dissipative equations of Korteweg-de Vries-Burgers type, Bull.Pol.Acad.Sc. Math. 32, 1984, 401-405. | Zbl | MR
9 , Neuron networks and Markov chains, Nauka, Moscow, 1985. | MR
10 , , Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D-Navier-Stokes equations, Comm. Pure Appl.Math. 38, 1985, 1-27. | Zbl | MR
11 , , , Attractors representing turbulent flows, Memoirs of AMS, 314, 1985. | Zbl | MR
12 , , Dimension de Hausdorff des attracteurs, C.R.Acad.Sc. Paris, 290 A-B, 1980, 1135-1138. | Zbl | MR
13 , Geometric Measure Theory, Springer 1969. | Zbl | MR
14 , , , , Asymptotic analysis of the Navier-Stokes equations, Physica 9D, 1983, 157-188. | Zbl | MR
15 , , , , variétés inertielles pour l'équation de Kuramoto-Sivashinski, C.R.Acad.Sc. Paris, 301, 1985, 285-288. | Zbl | MR
16 , , , Variétés inertielles des equations différentielles dissipatives, C.R. Acad.Sc. Paris, 301, 1985, 139-141. | Zbl | MR
17 , , Some analytic and geometric properties of the solutions of the Navier-Stokes equations, J.Math. pures appl. 58, 1979, 339-368. | Zbl | MR
18 , , A specifically nonlinear property of the operator semigroup of the Navier-Stokes equations, Comm. Pure Appl. Math. 35, 1982, 197-207. | Zbl | MR
19 , , On the Hausdorff dimension of an attractor for the two dimensional Navier-Stokes equations, Physics Letters 93A, 1983, 431-434. | MR
20 , A fixed point theorem for product spaces, Pacific. J. Math. 99, 1982, 327-335. | Zbl | MR
21 , , , , The Liapunov dimension of strange attractors, J.Diff.Eq. 49, 1983, 185-207. | Zbl | MR
22 , On the fractal dimension of attractors for viscous incompressible fluid flows, SIAM J.Math. Anal. /to appear/. | Zbl | MR
23 , , Propriétés des attracteurs associés à des équations hyperboliques non linéaires amorties, C.R.Acad.Sc. Paris, 300, 1985, 185-188. | Zbl | MR
24 , Comportement à l'infini des solutions des equations de Navier-Stokes et propriété des ensembles fonctionnels invariants ( ou attracteurs ), Ann. Inst. Fourier, 32, 1982, 1-37. | Numdam | Zbl | MR | EuDML
25 , Theory of Functional Differential Equations, Springer, 1977. | Zbl | MR
26 , , , An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory, Springer, 1984. | Zbl | MR
27 , , Dimension Theory, Princeton 1948. | Zbl | JFM
28 , Weakly contracting systems and attractors of Galerkin approximations of Navier-Stokes equations, Usp. Mat. Nauk, 36, 3, 1981, 243-244. | Zbl
29 -,,-, Weakly contracting systems and their attractors, Usp. Mat. Nauk, 37, 1, 1982, 166.
30 -,,-,On the dimension of attractors of k-contracting systems in an infinite dimensional space, Vestnik MGU, 3, 1983, 52-59. | Zbl | MR
31 -,,-, , On the dimension of attractors for a class of dissipative systems, Prikl. Mat. Mech., 46, 3, 1982, 374-381. limit | Zbl | MR
32 , Hyperbolic limit sets of evolution equations and Galerkin method, Usp. Mat. Nauk 35, 3, 1980. | Zbl | MR
33 -,,-, Hopf hypothesis for a class of chemical reaction equations, Zap. Nauch. Sem. LOMI, 110, 1981,57-73. | MR
34 , , Bounds on complexity in reaction-diffusion systems, Preprint IHES p/ 42, 1984. | Zbl | MR
35 , On a dynamical system generated by Navier-Stokes equations, Zap.Nauch.Sem. LOMI, 27, 1972, 91-115 (J. Soviet Math. 3, 1975, 455-479). | Zbl | MR
36 -,,-, On the finiteness of the dimension of bounded invariant sets for the Navier-Stokes equations and other related dissipative systems, Zap. Nauch. Sem. LOMI, 115, 1982, 137-155. | Zbl | MR
37 , Borne sur la dimension de Hausdorff de l'attracteur pour les équations de Navier-Stokes à deux dimensions, C. R. Acad. Ac. Paris, 298, 1984, 453-456. | Zbl | MR
38 , Some relations between dimension and Lyapunov exponents, Comm.Math.Phys. 81, 1981, 229-238. | Zbl | MR
39. , On characteristic exponents in turbulence, Comm.Math.Phys. 92, 1984, 473-480. | Zbl | MR
40 , Negatively invariant sets of compact maps and an extension of a theorem of Cartwright, J.Diff. Eq. 22, 1976, 331-348. | Zbl | MR
41 , On the dimension of the compact invariant sets of certain non-linear maps; Dynamical Systems and Turbulence, Warwick 1980, ed. by D.A. Rand, L.-S. Young, L.N.Math. 898, Springer 1981, 230-242. | Zbl | MR
42 , , , Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors, Physica 16D, 155-184, 1985. | Zbl | MR
43 , Differentiable dynamical systems and the problem of turbulence, Bull. AMS, 5, 1981, 29-42. | Zbl | MR
44 , Large volume limit of the distribution of characteristic exponents in turbulence, Comm. Math. Phys. 87, 1982, 287-302. | Zbl | MR
45 , Characteristic exponents for a viscous fluid subjected to time dependent forces, Comm. Math. Phys. 93, 1984, 285-300. | Zbl | MR
46 , , Some mathematical questions related to the MHD equations, Comm. Pure Appl. Math. 36, 1983, 635-664. | Zbl | MR
47 , Regular attractors of quasilinear hyperbolic systems with dissipation, Vestnik MGU 5, 1985, 74-77. | Zbl | MR
48 , Navier-Stokes equations and nonlinear functional analysis, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1983. | Zbl | MR
49 , Infinite dimensional dynamical systems in fluid mechanics, Proc. AMS Summer Research Institute "Nonlinear Functional Analysis and Applications", Berkeley 1983, ed. F. Browder. | Zbl
50 , Navier-Stokes Equations, Theory and Numerical Analysis, North Holland, 1984. | Zbl | MR





