Related papers: Random dynamics of two-dimensional stochastic seco…
Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a…
In this paper we develop two models for the steady states and evolution of two dimensional isothermal self gravitating and rotating incompressible gas which are based on the hydrodynamic equations for stratified fluid. The first model is…
We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…
A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…
In the causal theory of relativistic dissipative fluid dynamics, there are conditions on the equation of state and other thermodynamic properties such as the second-order coefficients of a fluid that need to be satisfied to guarantee that…
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect-product extension. Random…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under…
Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…
We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically $(s-1)$-growth with the parameter $s$…
The aim of these notes is to give an overview of the current results about existence and uniqueness of solutions for the stochastic Euler equation driven by a Brownian noise in a two-dimensional bounded domain.
We study the interaction of an incompressible fluid in two dimensions with an elastic structure yielding the moving boundary of the physical domain. The displacement of the structure is described by a linear viscoelastic beam equation. Our…
We observe the occurrence of a strange nonchaotic attractor in a periodically driven two-dimensional map, formerly proposed as a neuron model and a sequence generator. We characterize this attractor through the study of the Lyapunov…
We analyze a system of stochastic differential equations describing the joint motion of a massive (inert) particle in a viscous fluid in the presence of a gravitational field and a Brownian particle impinging on it from below, which…
In this paper, we propose a second-order dynamical system with a smoothing effect for solving paramonotone variational inequalities. Under standard assumptions, we prove that the trajectories of this dynamical system converges to a solution…
We consider the deterministic and stochastic versions of a first order non-autonomous differential equation which allows us to discuss the persistence of rivers ("fleuves") under noise.
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…
The density stratification in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting features. In particular, numerical and lab experiments show that, in two…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
We consider finite systems of interacting Brownian particles including active friction in the framework of nonlinear dynamics and statistical/stochastic theory. First we study the statistical properties for $1-d$ systems of masses connected…