Related papers: Stochastic Stability for Flows with Smooth Invaria…

In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this…

The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…

We investigate numerically in spherical geometry the interaction of stratification with precession. Both stable stratification and unstable stratification are studied. In the parameter regime we are concerned with, stable stratification…

We investigate the evolution of magnetohydrodynamic perturbations in presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with…

In this paper, we study stochastic stability of a dynamical system with shadowing property, which evolves under small random perturbation. We prove that time averages along the pseudo-trajectory converge with respect to stationary measure…

In this article, we consider the dynamics in a neighborhood of a quasi-periodic torus which is invariant by a Hamiltonian flow, we discuss several notions of stability and we prove several results of instability when the frequency of the…

We study stability of the sharp Poincar{\'e} constant of the invariant probability measure of a reversible diffusion process satisfying some natural conditions. The proof is based on the spectral interpretation of Poincar{\'e} inequalities…

This paper concerns a question that frequently occurs in various applications: Is any diffusive coupling of stable linear systems, also stable? Although it has been known for a long time that this is not the case, we shall identify a…

The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…

In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow. We provide examples where the stability (non-stability) is preserved under the Ricci flow and an example where the Ricci flow…

We present stability and recurrence results for a class of stochastic hybrid dynamical systems with oscillating flow maps. These results are developed by introducing averaging tools that parallel those already existing for ordinary…

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch,…

A new concept of {\em an evolution system of measures for stochastic flows} is considered. It corresponds to the notion of an invariant measure for random dynamical systems (or cocycles). The existence of evolution systems of measures for…

Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of…

We show that certain radially symmetric steady states of compressible viscous fluids in domains with inflow/outflow boundary conditions are unconditionally stable. This means that any not necessarily radially symmetric solution of the…

I shortly describe the main results on elastically driven instabilities and elastic turbulence in viscoelastic inertia-less flows with curved streamlines. Then I describe a theory of elastic turbulence and prediction of elastic waves at…

We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic…

We provide a general framework for the stability of solutions to stochastic partial differential equations with respect to perturbations of the drift. More precisely, we consider stochastic partial differential equations with drift given as…

We study the dynamics of small fluctuations about the uniform state of a crystal moving through a dissipative medium, e.g. a sedimenting colloidal crystal or a moving flux lattice, using a set of continuum equations for the displacement…

We establish short-time existence of a smooth solution to the surface diffusion equation with an elastic term and without an additional curvature regularization in three space dimensions. We also prove the asymptotic stability of strictly…