Samuel Walsh

Samuel Walsh is an Associate Professor in the Mathematics Department at the University of Missouri, within the College of Arts and Science. His research focuses on nonlinear partial differential equations, particularly those arising in fluid dynamics and water wave theory. He is actively involved in the academic community, organizing the Differential Equations Seminar and advising both graduate and undergraduate students.

• PhD in Applied Mathematics, Brown University, 2010
• BS in Mathematical Sciences, Carnegie Mellon University
• Former Courant Instructor, New York University

His primary research interests lie in nonlinear PDEs, especially water waves, steady waves, and dispersive systems. He investigates existence, stability, and qualitative properties of solutions in fluid mechanics, including solitary waves, internal waves, and vorticity-driven flows. His work often involves rigorous analysis of free boundary problems and global bifurcation theory.

Analysis of his recent publications reveals a strong focus on solitary and traveling water waves, particularly with vorticity, stratification, and interfacial effects. His work bridges rigorous mathematical analysis with physical fluid dynamics, emphasizing existence, stability, and asymptotic behavior. A recurring theme is the use of bifurcation theory and nonlinear functional analysis to construct and classify solutions to hydrodynamic PDEs.

Walsh has received research support from the National Science Foundation (grants DMS-1514950, DMS-1812436, DMS-2306243) and the Simons Foundation (Award 960210). These grants support his ongoing work in nonlinear wave phenomena and fluid dynamics.

• National Science Foundation: DMS-1514950, DMS-1812436, DMS-2306243
• Simons Foundation: Award 960210

He has advised numerous graduate students, including PhD candidates and MS students, many of whom have completed their degrees on topics related to water waves and PDE analysis. He also serves as the Math Competition Advisor at MU, mentoring undergraduates for the Putnam exam. Additionally, he mentored students in the 2012 Summer Undergraduate Research Experience (S.U.R.E.) at Courant.

Samuel Walsh organizes the Differential Equations Seminar at the University of Missouri, fostering academic exchange and collaboration in the field of PDEs and applied analysis.