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Elie Abdo

Publications and source records attributed to Elie Abdo.

22 records · Page 2Linked to original sources
arXiv2022

Unique Ergodicity in Stochastic Electroconvection

We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions, we define the corresponding Markov semigroup, and we study its Feller properties. When the noise forces enough modes in phase space, we obtain the uniqueness of the smooth invariant measure for the Markov transition kernels associated with the model.

math.AP↗
arXiv2022

Long Time Behavior of Solutions of an Electroconvection Model in $\R^2$

We consider a two dimensional electroconvection model which consists of a nonlinear and nonlocal system coupling the evolutions of a charge distribution and a fluid. We show that the solutions decay in time in $L^2(\Rr^2)$ at the same sharp rate as the linear uncoupled system. This is achieved by proving that the difference between the nonlinear and linear evolution decays at a faster rate than the linear evolution. In order to prove the sharp $L^2$ decay we establish bounds for decay in $H^2(\Rr^2)$ and a logarithmic growth in time of a quadratic moment of the charge density.

math.AP↗
arXiv2022

Invariant Measures for a Stochastic Electroconvection Model

We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions and we show that the corresponding Markov semigroup is weak Feller. We also prove the existence of invariant measures for the Markov transition kernels associated with the model.

math.AP↗