On the Domain of Analyticity and Small Scales for the Solutions of the Damped-driven 2D Navier-Stokes Equations [PDF]
arXiv, 2007 We obtain a logarithmically sharp estimate for the space-analyticity radius of the solutions of the damped-driven 2D Navier-Stokes equations with periodic boundary conditions and relate this to the small scales in this system. This system is inspired by the Stommel--Charney barotropic ocean circulation model.
arxiv
A new sharp estimate on the dimension of the attractor for the Dirichlet problem of the complex Ginzburg-Landau equation [PDF]
, 2008 Using the improved lower bound on the sum of the eigenvalues of the Dirichlet Laplacian proved by A. D. Melas (Proc. Amer. Math. Soc. \textbf{131} (2003) 631-636), we report a new and sharp estimate for the dimension of the global attractor associated to the complex Ginzburg-Landau equation supplemented with Dirichlet boundary conditions.
arxiv +1 more source
Finite dimensionality of 2-D micropolar fluid flow with periodic boundary conditions [PDF]
arXiv, 2007 This paper is devoted to describe the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate the number of them, we also estimate the dimension of the global attractor.
arxiv
Nonhyperbolicity of invariant measures on maximal attractor [PDF]
arXiv, 2008 The article states that for every compact manifold M of dimension 4 or higher there is an area U in a set of smooth diffeomorphisms over M such that every map f from U has local maximal partially hyperbolic attractor and nonatomic ergodic invariant measure on it where one of Lyapunov exponents vanish.
arxiv
Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential [PDF]
, 2009 A reaction-diffusion problem with an obstacle potential is considered in a bounded domain of $\R^N$. Under the assumption that the obstacle $\K$ is a closed convex and bounded subset of $\mathbb{R}^n$ with smooth boundary or it is a closed $n$-dimensional simplex, we prove that the long-time behavior of the solution semigroup associated with this ...
arxiv +1 more source
Finite speed of propagation for stochastic porous media equations [PDF]
arXiv, 2012 We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any continuous driving signal, thus including fractional Brownian motion for all Hurst parameters. The explicit estimates are
arxiv
Periodic and Almost Periodic Random Inertial Manifolds for Non-Autonomous Stochastic Equations [PDF]
arXiv, 2014 By the Lyapunov-Perron method,we prove the existence of random inertial manifolds for a class of equations driven simultaneously by non-autonomous deterministic and stochastic forcing. These invariant manifolds contain tempered pullback random attractors if such attractors exist.
arxiv
Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction [PDF]
arXiv, 2017 In this paper we study the long-time behavior of a nonlocal Cahn-Hilliard system with singular potential, degenerate mobility, and a reaction term. In particular, we prove the existence of a global attractor with finite fractal dimension, the existence of an exponential attractor, and convergence to equilibria for two physically relevant classes of ...
arxiv
Convergences of asymptotically autonomous pullback attractors towards semigroup attractors [PDF]
arXiv, 2017 For pullback attractors of asymptotically autonomous dynamical systems we study the convergences of their components towards the global attractors of the limiting semigroups. We use some conditions of uniform boundedness of pullback attractors, instead of uniform compactness conditions used in the literature.
arxiv
Birkhoff and Lyapunov spectra on planar self-affine sets [PDF]
arXiv, 2018 Working on strongly irreducible planar self-affine sets satisfying the strong open set condition, we calculate the Birkhoff spectrum of continuous potentials and the Lyapunov spectrum.
arxiv