The existence and dimension of the attractor for a 3D flow of a non-Newtonian fluid subject to dynamic boundary conditions. (English) Zbl 1541.35087
References:
| [1] | Chepyzhov, VV, Vishik, MI.Attractors for equations of mathematical physics. Providence (RI): American Mathematical Society; 2002. . · Zbl 0986.35001 |
| [2] | Chueshov, I, Lasiecka, I, Webster, JT.Attractors for delayed, nonrotational von Karman plates with applications to flow-structure interactions without any damping. Commun Partial Differ Equ. 2014;39(11):1965-1997. · Zbl 1299.74053 |
| [3] | Chueshov, I, Lasiecka, I.Von Karman evolution equations. New York (NY): Springer; 2010. · Zbl 1298.35001 |
| [4] | Robinson, JC.Dimensions, embeddings, and attractors. Cambridge: Cambridge University Press; 2011. . · Zbl 1222.37004 |
| [5] | Temam, R.Infinite-dimensional dynamical systems in mechanics and physics. 2nd ed.New York: Springer-Verlag; 1997. . · Zbl 0871.35001 |
| [6] | Ilyin, A, Patni, K, Zelik, S.Upper bounds for the attractor dimension of damped Navier-Stokes equations in \(\mathbb{R}^2 \). Discrete Contin Dyn Syst. 2016;36(4):2085-2102. · Zbl 1327.35036 |
| [7] | Ilyin, A, Kostianko, A, Zelik, S.Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations. Phys D. 2022;432.Paper No. 133156, 13. · Zbl 1490.35273 |
| [8] | Ladyzhenskaya, OA.New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problems for them. Tr Mat Inst Steklova. 1967;102:85-104. · Zbl 0202.37802 |
| [9] | Málek, J, Rajagopal, KR. Mathematical issues concerning the Navier-Stokes equations and some of its generalizations. In: Evolutionary equations. Vol. II, Handb. Differ. Equ. Amsterdam: Elsevier/North-Holland; 2005. p. 371-459. · Zbl 1095.35027 |
| [10] | Abbatiello, A, Bulíček, M, Maringová, E.On the dynamic slip boundary condition for Navier-Stokes-like problems. Math Models Methods Appl Sci. 2021;31(11):2165-2212. · Zbl 1478.35172 |
| [11] | Maringová, E. Mathematical analysis of models arising in continuum mechanics with implicitly given rheology and boundary conditions [PhD thesis]. Faculty of Mathematics and Physics, Charles University; 2019. |
| [12] | Pražák, D, Zelina, M. On the uniqueness of the solution and finite-dimensional attractors for the 3D flow with dynamic boundary condition. Submitted. · Zbl 1525.76024 |
| [13] | Bulíček, M, Ettwein, F, Kaplický, P, et al. The dimension of the attractor for the 3D flow of a non-Newtonian fluid. Commun Pure Appl Anal. 2009;8(5):1503-1520. · Zbl 1200.37074 |
| [14] | Kaplický, P, Pražák, D.Lyapunov exponents and the dimension of the attractor for 2D shear-thinning incompressible flow. Discrete Contin Dyn Syst. 2008;20(4):961-974. · Zbl 1151.37060 |
| [15] | Pražák, D, Žabenský, J.On the dimension of the attractor for a perturbed 3D Ladyzhenskaya model. Cent Eur J Math. 2013;11(7):1264-1282. · Zbl 1358.35130 |
| [16] | Málek, J, Pražák, D.Large time behavior via the method of l-trajectories. J Differ Equ. 2002;181(2):243-279. · Zbl 1187.37113 |
| [17] | Bulíček, M, Málek, J, Pražák, D.On the dimension of the attractor for a class of fluids with pressure dependent viscosities. Commun Pure Appl Anal. 2005;4(4):805-822. · Zbl 1125.37057 |
| [18] | Pražák, D, Zelina, M. On linearization principle for Navier-Stokes system with dynamic slip boundary condition. Accepted to CPAA (Comm. Pure Appl. Anal.). · Zbl 1525.76024 |
| [19] | Bensoussan, A, Da Prato, G, Delfour, MC, et al. Representation and control of infinite dimensional systems. 2nd ed. Boston (MA): Birkhäuser Boston, Inc.; 2007. . · Zbl 1117.93002 |
| [20] | Triebel, H.Interpolation theory, function spaces, differential operators. Amsterdam (NY): North-Holland Pub. Co; 1978. · Zbl 0387.46033 |
| [21] | Lasiecka, I, Triggiani, R.Domains of fractional powers of matrix-valued operators: a general approach. Oper Theory Adv Appl. 2015;250:297-309. · Zbl 1360.47009 |
| [22] | Boyer, F, Fabrie, P.Mathematical tools for the study of the incompressible Navier-Stokes equations and related models. New York: Springer; 2013. . · Zbl 1286.76005 |
| [23] | Bulíček, M, Málek, J, Rajagopal, KR.Navier’s slip and evolutionary Navier-Stokes-like systems with pressure and shear-rate dependent viscosity. Indiana Univ Math J. 2007;56(1):51-86. · Zbl 1129.35055 |
| [24] | Constantin, C, Foias, P.Navier-Stokes equations. Chicago: University of Chicago Press; 1988. · Zbl 0687.35071 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
