6 papers · 1 filter
On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains
Elie Abdo, Quyuan Lin
We investigate new properties of the fractional Dirichlet Laplacian on smooth bounded domains and establish fractional product estimates and nonlinear Poincaré inequalities. We als…
On the Three-dimensional Nernst-Planck-Boussinesq System
Elie Abdo, Ruimeng Hu, Quyuan Lin
In this paper, we analyze a three-dimensional Nernst-Planck-Boussinesq (NPB) system that describes ionic electrodiffusion in an incompressible viscous fluid. This new model incorpo…
On the global well-posedness and Gevrey regularity of some electrodiffusion models
Elie Abdo, Fizay-Noah Lee, Weinan Wang
We consider the Nernst-Planck equations describing the nonlinear time evolution of multiple ionic concentrations in a two-dimensional incompressible fluid. The velocity of the flui…
Unique Ergodicity in Stochastic Electroconvection
Elie Abdo, Nathan Glatt-Holtz, Mihaela Ignatova
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 prov…
Invariant Measures for a Stochastic Electroconvection Model
Elie Abdo, Mihaela Ignatova
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 prov…
On Electroconvection in Porous Media
Elie Abdo, Mihaela Ignatova
We address existence, uniqueness and analyticity of solutions of an electroconvection model in porous media.