43 citations · 75 across the 18 of their papers we have counts for
22 papers
Real analytic solutions to the divergence equation
Chi Hin Chan, Jun-Shuo Chen, Cheng-Fang Su
In this paper, we develop a differential-topological method to yield explicit real analytic solutions to the divergence equation on any annali $A(R_1…
Thin shell limit and the derivation of the viscosity operator on the ellipsoid
Chi Hin Chan, Magdalena Czubak, Padi Fuster Aguilera
In this paper we derive four new candidates for an intrinsic viscosity operator on an ellipsoid by using the heuristic of the thin shell limit along the scaling direction of the el…
NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements
Khemraj Shukla, Zongren Zou, Chi Hin Chan +3
Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due…
The Meyers-Serrin theorem on Riemannian manifolds: a survey
Chi Hin Chan, Magdalena Czubak
We revisit the questions of density of smooth functions, and differential forms, in Sobolev spaces on Riemannian manifolds. We carefully show equivalence of weak covariant derivati…
The Gauss formulas for Laplacians on submanifolds
Chi Hin Chan, Magdalena Czubak
There are several types of Laplacians of a vector field on a Riemannian manifold. These include the Bochner and the Hodge Laplacian. The Gauss formula for the Levi-Civita connectio…
The restriction problem on the ellipsoid
Chi Hin Chan, Magdalena Czubak, Tsuyoshi Yoneda
Following a restriction argument in the Euclidean space, we derive a geometric invariant formula for a possible viscosity operator for an incompressible fluid flow on an ellipsoid…