5 citations · 10 across the 7 of their papers we have counts for
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Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs
Seungchan Ko, Seok-Bae Yun, Youngjoon Hong
In this paper, we perform the convergence analysis of unsupervised Legendre--Galerkin neural networks (ULGNet), a deep-learning-based numerical method for solving partial different…
Quasi-Monte Carlo finite element approximation of the Navier-Stokes equations with initial data modeled by log-normal random fields
Seungchan Ko, Guanglian Li, Yi Yu
In this paper, we analyze the numerical approximation of the Navier-Stokes problem over a bounded polygonal domain in , where the initial condition is modeled by a lo…
Some Liouville-type theorems for the stationary 3D magneto-micropolar fluids
Jae-Myoung Kim, Seungchan Ko
In this paper we prove some Liouville-type theorems for the stationary magneto-micropolar fluids under suitable conditions in three space dimensions. We first prove that the soluti…
Upper and lower bounds of convergence rates for strong solutions of the generalized Newtonian fluids with non-standard growth conditions
Jae-Myoung Kim, Seungchan Ko
We consider the motion of an incompressible shear-thickening power-law-like non-Newtonian fluid in with a variable power-law index. This system of nonlinear partial different…
Temporal decay of strong solutions for generalized Newtonian fluids with variable power-law index
Seungchan Ko
We consider the motion of a power-law-like generalized Newtonian fluid in R^3, where the power-law index is a variable function. This system of nonlinear partial differential equat…