Research

My research concerns the analysis and computation of singularly perturbed partial differential equations, with particular emphasis on singular layer phenomena and vanishing-parameter limits arising in fluid flow and related systems.

I am interested in how small physical parameters, such as viscosity or diffusivity, give rise to multi-scale structures that fundamentally influence both the analytical properties of solutions and the performance of numerical methods.

A central theme of my work is the development of explicit asymptotic descriptions and correctors that capture the dominant structure of solutions in singular regimes. These constructions provide a foundation for rigorous analytical results and also guide the design of numerical methods whose performance remains robust as perturbation parameters tend to zero. 

More recently, my research has extended to include structure-preserving and analysis-informed learning methods and hybrid numerical approaches for stiff partial differential equations. These hybrid frameworks combine asymptotic layer decomposition, conservative discretizations, and learning-based components, with the goal of achieving uniform accuracy in singular limits, particularly in regimes where standard numerical or learning-based solvers often fail.

Singular Perturbations and Boundary Layers 

I study boundary, corner, and interior layers arising in viscous and diffusive limits of partial differential equations. This includes problems involving curved or non-smooth domains, ill-prepared initial or boundary data, and multiple interacting scales. My work aims to clarify how such structures influence stability, convergence, and accuracy in both analysis and computation of solutions.

Structure-preserving and Analysis-informed Hybrid Methods

A recent focus of my research is the development of hybrid numerical frameworks that integrate asymptotic analysis with conservative discretizations and learning-based components. Rather than treating learning methods as black-box solvers, these approaches use asymptotic layer decomposition to guide and constrain the approximation, yielding methods whose performance is robust with respect to small parameters.

Rotating and Stratified Flows

I am particularly interested in rotating and stratified flow models, including simplified forms of the primitive equations. In such systems, rotation and stratification introduce additional scales and anisotropies that lead to complex layer interactions and singular limits.

This setting provides a natural framework in which classical singular perturbation theory, boundary layer analysis, and structure-preserving computational methods intersect, and serves as a testing ground for analysis-informed numerical and learning-based approaches in geophysical fluid dynamics.

Publications related to this research

Selected publications that illustrate aspects of this work are listed on the Publications page. A complete list of publications is available via my curriculum vitae.