The concept of the slow invariant manifold is recognized as the central idea underpinning a
transition from micro to macro and model reduction in kinetic theories. We present the …

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The intriguing figure from the previous page presents a visualization of the type of manifolds
this monograph is concerned with. First, obtained as a graph over some chosen linearized …

This book is devoted to the subject commonly called Chaotic Dynamics, namely the study of
complicated behavior in time of maps and? ows, called dynamical systems. The theory of …

We present numerical results and computer assisted proofs of the existence of periodic
orbits for the Kuramoto--Sivashinky equation. These two results are based on writing down …

We present a class of efficient parametric closure models for 1D stochastic Burgers
equations. Casting it as statistical learning of the flow map, we derive the parametric form by …

A postprocessing technique, developed earlier for spectral methods, is extended here to
Galerkin finite-element methods for dissipative evolution partial differential equations. The …

We revisit the postprocessing algorithm and give a justification from a classical truncation
analysis point of view. We assume a perturbation expansion for the high frequency mode …

This paper introduces an explicit numerical criterion for the stabilization of steady state
solutions of the Navier-Stokes equations (NSE) with linear feedback control. Given a linear …

综述近年来非线性动力系统降维理论与方法的研究现状. 主要介绍非线性动力系统现有降维方法
的基本思想, 特点与局限性; 这些方法包括: 基于中心流形理论的降维方法, Lyapunov-Schmidt …