Related papers: Ergodic theory for energetically open compressible…
The idea of a parsing of a stationary process according to a collection of words is introduced, and the basic framework required for the asymptotic analysis of these parsings is presented. We demonstrate how the pointwise ergodic theorem…
The present paper is concerned with an inviscid limit problem of radially symmetric stationary solutions for an exterior problem in $\mathbb{R}^n (n\ge 2)$ to compressible Navier-Stokes equation, describing the motion of viscous barotropic…
A method for obtaining simple criteria for instabilities in kinetic theory is described and outlined, specifically for the relativistic Vlasov-Maxwell system. An important ingredient of the method is an analysis of a parametrized set of…
The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous…
We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. Motivated by recent applications in the…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
We give a short proof that the ergodic sums of $\mathcal{C}^1$ observables for a $\mathcal{C}^1$ flow on $\mathbb{T}^2$ admitting a closed transversal curve whose Poincar\'e map has constant type rotation number have growth deviating at…
We consider Bourgain's ergodic theorem regarding arithmetic averages in the cases where quantitative mixing is present in the dynamical system. Focusing on the case of the horocyclic flow, those estimates allows us to bound from above the…
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations for compressible fluids in $\mathbb{R}^3$. Motivated by the Kolmogorov hypothesis (1941) for incompressible flow, we introduce a Kolmogorov-type…
It is well-known that a strict analogue of the Birkhoff Ergodic Theorem in infinite ergodic theory is trivial; it states that for any infinite-measure-preserving ergodic system the Birkhoff average of every integrable function is almost…
It is known that a gambler repeating a game with positive expected value has a positive probability to never go broke. We use the mass transport method to prove the generalization of this fact where the gains from the bets form a…
We study the ergodic properties of generic continuous dynamical systems on compact manifolds. As a main result we prove that generic homeomorphisms have convergent Birkhoff averages under continuous observables at Lebesgue almost every…
This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…
In this paper, we study the pointwise convergence of centain continuous-time polynomial ergodic averages. Our approach is based on the topological models of measurable flows. One of the main results of this paper is as follows: Let $a\in…
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…
We show that a $k$-linear pointwise ergodic theorem on an ergodic measure-preserving system implies a uniform $k$-linear nilsequence Wiener-Wintner theorem on that system. The assumption is known to hold for arbitrary systems and $k=2$ (due…
We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving $\|\sum_{k=1} ^nf\circ \theta^k\|_2$, improving previous results. Then, using known results on martingale…
Asymptotic behavior of the three-dimensional stochastic Navier-Stokes equations with Markov switching in additive noises is studied for incompressible fluid flow in a bounded domain in the three-dimensional space. To study such a system, we…
The kinetic theory for a fluid of hard spheres which undergo endothermic and/or exothermic reactions with mass transfer is developed. The exact balance equations for concentration, density, velocity and temperature are derived. The Enskog…
Given an obstacle in $\mathbb{R}^3$ and a non-zero velocity with small amplitude at the infinity, we construct the unique steady Boltzmann solution flowing around such an obstacle with the prescribed velocity as $|x|\to \infty$, which…