1 citations · 2 across the 21 of their papers we have counts for
23 papers
On a Multispecies Electrodiffusion Model in Higher-Dimensional Porous Media
Elie Abdo, Christofer Ghazale
We consider the Nernst--Planck--Darcy system describing the electrodiffusion of ionic species with arbitrary valences and different diffusivities, transported by a Darcy flow d…
Entropy Analysis of some Active Scalar Equations
Elie Abdo
We study a broad family of active scalar equations with fractional dissipation on and prove that their entropy diverges to at a sharp rate of order $\log t…
On the Non-isothermal Nernst-Planck-Navier-Stokes System
Elie Abdo, Quyuan Lin
Electrodiffusion has been extensively studied in the isothermal setting, whereas the mathematical theory of thermally coupled electrodiffusion remains comparatively underdeveloped.…
EML Trees Are Universal Approximators
Joe Germany, Elie Abdo, Joseph Bakarji
The recently introduced EML (Exp-Minus-Log) function acts as continuous analogue of NAND gates, providing a compositional building block capable of representing elementary function…
Long time dynamics of the Nernst-Planck-Darcy System on
Elie Abdo, Joe Germany, Mohammad Khalil Hamdan +1
We study ionic electrodiffusion modeled by the Nernst--Planck equations describing the evolution of ionic species in a three-dimensional incompressible fluid flowing through a…
Convergence Analysis of PINNs for Fractional Diffusion Equations in Bounded Domains
Elie Abdo, Lihui Chai, Ruimeng Hu +1
We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Lapl…
Well-posedness and ill-posedness of the primitive equations with fractional horizontal dissipation
Elie Abdo, Quyuan Lin, Changhui Tan
The primitive equations (PE) are a fundamental model in geophysical fluid dynamics. While the viscous PE are globally well-posed, their inviscid counterparts are known to be ill-po…
Electroconvection in a Magnetic Field
Elie Abdo, Peter Constantin, Mihaela Ignatova +1
Electroconvection in a porous medium under a strong transversal magnetic field is described by an active scalar equation for the charge density. The equation has global weak soluti…
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…
Long Time Dynamics Of The Three-dimensional Nernst-Planck-Darcy Model
Elie Abdo, Đorđe Nikolić
We consider an electrodiffusion model describing the evolution of ionic species in a three-dimensional fluid flowing through a porous medium and forced by added body charges. W…
Error estimates of physics-informed neural networks for approximating Boltzmann equation
Elie Abdo, Lihui Chai, Ruimeng Hu +1
Motivated by the recent successful application of physics-informed neural networks (PINNs) to solve Boltzmann-type equations [S. Jin, Z. Ma, and K. Wu, J. Sci. Comput., 94 (2023),…
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…
Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations
Elie Abdo, Fizay-Noah Lee
We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to…
On the space-time analyticity of the Keller-Segel-Navier-Stokes system
Elie Abdo, Zhongtian Hu
In this paper, we study the coupled Keller-Segel-Navier-Stokes system, which models chemotaxis occuring in ambient viscous fluid. We consider this nonlinear, nonlocal system on a p…
A PDE Perspective on Approximating Nonlocal Periodic Operators with Applications on Neural Networks for Critical SQG Equations
Elie Abdo, Ruimeng Hu, Quyuan Lin
Nonlocal periodic operators in partial differential equations (PDEs) pose challenges in constructing neural network solutions, which typically lack periodic boundary conditions. In…
On the Long-time Dynamics and Ergodicity of the Stochastic Nernst-Planck-Navier-Stokes System
Elie Abdo, Ruimeng Hu, Quyuan Lin
We consider an electrodiffusion model that describes the intricate interplay of multiple ionic species with a two-dimensional, incompressible, viscous fluid subjected to stochastic…
Long time dynamics of a fractional dissipative model of electroconvection in bounded domains
E. Abdo, M. Ignatova
We consider a nonlocal nonlinear model with fractional diffusion motivated by studies of electroconvection phenomena in incompressible viscous fluids. We address the global well-po…
On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions
Elie Abdo, Weinan Wang
We consider the inhomogeneous heat equation on the half-space with Neumann boundary conditions. We prove a space-time Gevrey regularity of the solution, with a…
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…
Long Time Behavior of Solutions of an Electroconvection Model in
Elie Abdo, Mihaela Ignatova
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 t…
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.