9 citations · 27 across the 24 of their papers we have counts for
5 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…
Regularization by noise for the inviscid primitive equations
Ruimeng Hu, Quyuan Lin, Rongchang Liu
The deterministic inviscid primitive equations (also called the hydrostatic Euler equations) are known to be ill-posed in Sobolev spaces and in Gevrey classes of order strictly gre…
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…
Global well-posedness and enhanced dissipation for the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise
Quyuan Lin, Rongchang Liu, Weinan Wang
In this paper, we consider the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise. By assuming the ionic species have the same diffusivity and opposite valenc…
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…