Displaying similar documents to “Strong hydrodynamic limit for attractive particle systems on ℤ .”

On exponential convergence to a stationary measure for a class of random dynamical systems

Sergei B. Kuksin (2001)

Journées équations aux dérivées partielles

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For a class of random dynamical systems which describe dissipative nonlinear PDEs perturbed by a bounded random kick-force, I propose a “direct proof” of the uniqueness of the stationary measure and exponential convergence of solutions to this measure, by showing that the transfer-operator, acting in the space of probability measures given the Kantorovich metric, defines a contraction of this space.

Convex hulls, Sticky particle dynamics and Pressure-less gas system

Octave Moutsinga (2008)

Annales mathématiques Blaise Pascal

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We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities u 0 with negative jumps. We show the existence of a stochastic process and a forward flow φ satisfying X s + t = φ ( X s , t , P s , u s ) and d X t = E [ u 0 ( X 0 ) / X t ] d t , where P s = P X s - 1 is the law of X s and u s ( x ) = E [ u 0 ( X 0 ) / X s = x ] is the velocity of particle x at time s ≥ 0 . Results on the flow characterization and Lipschitz continuity are also given. Moreover, the map ( x , t ) ↦ M ( x , t ) : = P ( X t ≤ x ) is the entropy solution of a scalar conservation...

Strong and weak solutions to stochastic inclusions

Michał Kisielewicz (1995)

Banach Center Publications

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Existence of strong and weak solutions to stochastic inclusions x t - x s ∈ ∫ s t F τ ( x τ ) d τ + ∫ s t G τ ( x τ ) d w τ + ∫ s t ∫ ℝ n H τ , z ( x τ ) q ( d τ , d z ) and x t - x s ∈ ∫ s t F τ ( x τ ) d τ + ∫ s t G τ ( x τ ) d w τ + ∫ s t ∫ | z | ≤ 1 H τ , z ( x τ ) q ( d τ , d z ) + ∫ s t ∫ | z | > 1 H τ , z ( x τ ) p ( d τ , d z ) , where p and q are certain random measures, is considered.

On recent progress for the stochastic Navier Stokes equations

Jonathan Mattingly (2003)

Journées équations aux dérivées partielles

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We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations. Since our desire is to make the core ideas clear, we will mostly work with a specific example : the stochastically forced Navier Stokes equations. To further clarify ideas, we will also examine in detail a toy problem. A few general theorems are given. Spatial regularity, ergodicity,...