43 citations · 102 across the 18 of their papers we have counts for
25 papers
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…
Dichotomy Results for the Electromagnetic Schrödinger Equation
Magdalena Czubak, Ian Miller, Svetlana Roudenko
The electromagnetic nonlinear Schrödinger (emNLS) equation is a variant of the well-studied nonlinear Schrödinger equation. In this article, we consider questions of global existen…
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…
Blowing Up Solutions to the Zakharov System for Langmuir Waves
Yuri Cher, Magdalena Czubak, Catherine Sulem
Langmuir waves take place in a quasi-neutral plasma and are modeled by the Zakharov system. The phenomenon of collapse, described by blowing up solutions plays a central role in th…