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Exponential Attractors in Generalized Relativistic Billiards
Communications in Mathematical Physics, 2004A generalized relativistic billiard is the following dynamical system: a particle moves under the influence of some force fields in the interior of a domain with pseudo-Riemannian metric, and as the particle hits the boundary of the domain, its velocity is transformed as if the particle underwent an elastic collision with a moving wall, considered in ...
L.D. Pustyl’nikov, M.V. Deryabin
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A uniformly exponential random forward attractor which is not a pullback attractor
Archiv der Mathematik, 2002The author constructs an example of a random forward attractor for a random dynamical system (RDS) that is not a pullback attractor which is one of 3 possible notions of an attractor one can naturally define for RDS (and which all coincide for deterministic dynamical systems).
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Exponential attractors for semigroups in Banach spaces
Nonlinear Analysis: Theory, Methods & Applications, 2012Abstract Let { S ( t ) } t ⩾ 0 be a semigroup on a Banach space X , and A be the global attractor for { S ( t ) } t ⩾ 0 . We assume that there exists a T ∗ such that S ≜ S ( T ∗ ) is of class C 1 on a bounded absorbing set B ϵ 0
Chengkui Zhong, Yansheng Zhong
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Approximation of exponential order of the attractor of a turbulent flow
Physica D: Nonlinear Phenomena, 1994We consider the two-dimensional Navier-Stokes equations with periodic boundary conditions, describing the evolution of homogeneous flows. We construct approximate inertial manifolds (AIMs) whose order decreases exponentially fast with respect to the dimension of the manifold. We recall that an AIM is a smooth manifold of solutions \({\mathcal M}\) such
T. Dubois, Arnaud Debussche
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Exponential attractors and their relevance to fluid dynamics systems
Physica D: Nonlinear Phenomena, 1993This paper investigates the theory of exponential attractors and its significance in infinite dimensional dynamical systems. The authors study a general class of parabolic P.D.E. with emphasis given to the 2D Navier- Stokes equations. Kuramoto-Sivashinsky equation is also studied briefly.
Ciprian Foias +6 more
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Finite‐dimensional attractors and exponential attractors for degenerate doubly nonlinear equations
Mathematical Methods in the Applied Sciences, 2009AbstractWe consider the following doubly nonlinear parabolic equation in a bounded domain Ω⊂ℝ3:where the nonlinearityfis allowed to have a degeneracy with respect to ∂tuof the form ∂tu|∂tu|pat some pointsx∈Ω.Under some natural assumptions on the nonlinearitiesfandg, we prove the existence and uniqueness of a solution of that problem and establish the ...
Efendiev, M, Zelik, S
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Random Exponential Attractor for the 3D Non-autonomous Stochastic Damped Navier–Stokes Equation
Journal of Dynamics and Differential Equations, 2021Zongfei Han, Shengfan Zhou
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, 2015
We prove exponential decay of correlations for a class of $${C^{1+\alpha}}$$C1+α uniformly hyperbolic skew product flows, subject to a uniform nonintegrability condition.
V. Araújo, I. Melbourne
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We prove exponential decay of correlations for a class of $${C^{1+\alpha}}$$C1+α uniformly hyperbolic skew product flows, subject to a uniform nonintegrability condition.
V. Araújo, I. Melbourne
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Exponential attractors for a conserved phase-field system with memory
Physica D: Nonlinear Phenomena, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. GATTI +2 more
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SIAM Journal on Mathematical Analysis, 2003
Summary: We prove that the uniform attractor for the Navier-Stokes equations of compressible flow with quasi-periodic external forces has finite fractal dimension. As a byproduct of our analysis, we also obtain the existence of finite-dimensional exponential attractors for the Navier-Stokes system.
David Hoff, Mohammed Ziane
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Summary: We prove that the uniform attractor for the Navier-Stokes equations of compressible flow with quasi-periodic external forces has finite fractal dimension. As a byproduct of our analysis, we also obtain the existence of finite-dimensional exponential attractors for the Navier-Stokes system.
David Hoff, Mohammed Ziane
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