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My research spans singular perturbation theory, boundary and interior layer analysis, and structure-preserving numerical and learning-based methods for stiff partial differential equations. Selected publications that represent these themes are listed below. A complete list of publications is available in my curriculum vitae.
My research spans singular perturbation theory, boundary and interior layer analysis, and structure-preserving numerical and learning-based methods for stiff partial differential equations. Selected publications that represent these themes are listed below. A complete list of publications is available in my curriculum vitae.
Selected Publications
Selected Publications
Singular perturbations and boundary layers with M. Hamouda, C.-Y. Jung, and R. Temam, Springer, 2018.
A reference monograph on singular perturbation problems and boundary layers arising in fluid dynamics and related systems.
Singular perturbations and boundary layers with M. Hamouda, C.-Y. Jung, and R. Temam, Springer, 2018.
A reference monograph on singular perturbation problems and boundary layers arising in fluid dynamics and related systems.
Singular-layer PINN methods for Burgers’ equation with T.-Y. Chang, Y. Hong, and C.-Y. Jung, Accepted for publication in Pure and Applied Functional Analysis.
Develops structure-preserving and analysis-informed learning methods for resolving interior layers in the small-viscosity regime.
Singular-layer PINN methods for Burgers’ equation with T.-Y. Chang, Y. Hong, and C.-Y. Jung, Accepted for publication in Pure and Applied Functional Analysis.
Develops structure-preserving and analysis-informed learning methods for resolving interior layers in the small-viscosity regime.
Physics-informed neural network approach for singular layers in periodic parallel pipe flows with M. Moon, Y. Hong, and C.-Y. Jung, Submitted.
Integrates asymptotic analysis with learning-based methods for viscous boundary layers and vorticity layers.
Physics-informed neural network approach for singular layers in periodic parallel pipe flows with M. Moon, Y. Hong, and C.-Y. Jung, Submitted.
Integrates asymptotic analysis with learning-based methods for viscous boundary layers and vorticity layers.
Finite volume neural networks for singularly perturbed boundary value problems with J. Kim, Submitted.
Develops flux-preserving hybrid learning-based methods that are robust in small-parameter regimes.
Finite volume neural networks for singularly perturbed boundary value problems with J. Kim, Submitted.
Develops flux-preserving hybrid learning-based methods that are robust in small-parameter regimes.
Vanishing viscosity limit of some symmetric flows with J. Kelliher, M. Lopes Filho, A. Mazzucato, H. Nussenzveig Lopes, Annales de l’Institut Henri Poincaré C: Analyse Non Linéaire.
Provides rigorous analysis of vanishing viscosity limit and boundary layer formation.
Vanishing viscosity limit of some symmetric flows with J. Kelliher, M. Lopes Filho, A. Mazzucato, H. Nussenzveig Lopes, Annales de l’Institut Henri Poincaré C: Analyse Non Linéaire.
Provides rigorous analysis of vanishing viscosity limit and boundary layer formation.
The 3D Euler equations with inflow, outflow and vorticity boundary conditions with J. Kelliher, and A. Mazzucato, Journal de Mathématiques Pures et Appliquées.
Establishes rigorous well-posedness results for ideal flows at the inviscid limit.
The 3D Euler equations with inflow, outflow and vorticity boundary conditions with J. Kelliher, and A. Mazzucato, Journal de Mathématiques Pures et Appliquées.
Establishes rigorous well-posedness results for ideal flows at the inviscid limit.
Recent progresses in boundary layer theory with C.-Y. Jung and R. Temam, Discrete and Continuous Dynamical Systems, Series A.
Analyzes geometric effects on asymptotic boundary layer structure.
Recent progresses in boundary layer theory with C.-Y. Jung and R. Temam, Discrete and Continuous Dynamical Systems, Series A.
Analyzes geometric effects on asymptotic boundary layer structure.
Enriched Finite Volume approximations of the plane-parallel flow at a small viscosity with C.-Y. Jung and H. Lee, Journal of Scientific Computing.
Develops structure-preserving hybrid numerical methods for stiff partial differential equations.
Enriched Finite Volume approximations of the plane-parallel flow at a small viscosity with C.-Y. Jung and H. Lee, Journal of Scientific Computing.
Develops structure-preserving hybrid numerical methods for stiff partial differential equations.
Complete List of Publications
Complete List of Publications
A complete and up-to-date list of publications, including preprints and accepted articles, is available in my curriculum vitae.
A complete and up-to-date list of publications, including preprints and accepted articles, is available in my curriculum vitae.
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