Results 11 to 20 of about 169 (41)

The number of degrees of freedom for the 2D Navier-Stokes equation: a connection with Kraichnan's theory of turbulence [PDF]

arXiv, 2021
We estimate the number of degrees of freedom of solutions of the 2D Navier-Stokes equation, proving that its mathematical analog, the number of determining modes, is bounded by the Kraichnan number squared. In particular, this provides new bounds on the number of determining modes in term of the Grashof number for solutions that are not highly ...
arxiv  

Long-time Behavior for a Nonlinear Plate Equation with Thermal Memory [PDF]

J. Math. Anal. Appl., Vol.348 (2008), 650-670, 2008
We consider a nonlinear plate equation with thermal memory effects due to non-Fourier heat flux laws. First we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we use a suitable Lojasiewicz--Simon type inequality to show the convergence of global solutions to single steady states as time goes ...
arxiv   +1 more source

Pullback attractors for fractional lattice systems with delays in weighted space

Open Mathematics
This article deals with the asymptotic behavior of fractional lattice systems with time-varying delays in weighted space. First, we establish some sufficient conditions for the existence and uniqueness of solutions.
Li Xintao, Wang Shengwen
doaj   +1 more source

Lyapunov exponents and synchronisation by noise for systems of SPDEs [PDF]

arXiv, 2022
Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the invariant measure, with careful control on the resulting error terms.
arxiv  

Limiting dynamics for stochastic complex Ginzburg-Landau systems with time-varying delays on unbounded thin domains

Demonstratio Mathematica
This study deals with the limiting dynamics for stochastic complex Ginzburg-Landau systems with time-varying delays and multiplicative noise on unbounded thin domains. We first prove the existence and uniqueness of pullback tempered random attractors for
Li Xintao, Pan Shiyao
doaj   +1 more source

Periodic measures of fractional stochastic discrete wave equations with nonlinear noise

Demonstratio Mathematica
The primary focus of this work lies in the exploration of the limiting dynamics governing fractional stochastic discrete wave equations with nonlinear noise.
Li Xintao, She Lianbing, Yao Jingjing
doaj   +1 more source

SPDE in Hilbert Space with Locally Monotone Coefficients [PDF]

J. Funct. Anal. 259 (2010), 2902--2922, 2010
In this paper we prove the existence and uniqueness of strong solutions for SPDE in Hilbert space with locally monotone coefficients, which is a generalization of the classical result of Krylov and Rozovskii for monotone coefficients. Our main result can be applied to different types of SPDEs such as stochastic reaction-diffusion equations, stochastic ...
arxiv   +1 more source

Fractal Hypersurfaces, Wavelet Sets and Affine Weyl Groups [PDF]

arXiv, 2013
In these lecture notes we present connections between the theory of iterated function systems, in particular those attractors that are graphs of multivariate real-valued fractal functions, foldable figures and affine Weyl groups, and wavelet sets.
arxiv  

Complexity for extended dynamical systems [PDF]

, 2006
We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, epsilon-entropy and topological entropy per unit time and volume have been introduced previously. In this paper we use the notion of Kolmogorov complexity to introduce, for extended dynamical systems, a notion of ...
arxiv   +1 more source

Large time behavior of solutions to a dissipative Boussinesq system [PDF]

arXiv, 2006
In this article we consider the Boussinesq system supplemented with some dissipation terms. These equations model the propagation of a waterwave in shallow water. We prove the existence of a global smooth attractor for the corresponding dynamical system.
arxiv