معرفی
Ian Tice is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University. His research focuses on the analysis of nonlinear partial differential equations, particularly those arising in physics such as interfacial fluid mechanics and the Ginzburg-Landau model of superconductivity.
Education:
- Ph.D. in Mathematics, Courant Institute, New York University
- Postdoctoral Appointments: Université Paris-Est Créteil, Laboratoire d'Analyse et de Mathématiques Appliquées
- Postdoctoral Appointments: Brown University, Division of Applied Mathematics
Research Interests:
Ian Tice specializes in the analysis of nonlinear partial differential equations, with particular focus on free and moving boundary problems, fluid mechanics, and vortices in superconductors. His work often involves the calculus of variations and tools from function space theory. He studies how singularities behave in physical systems, including surfaces of discontinuity in fluids and point singularities known as vortices in superconductors.
Recent Research Trends:
Professor Tice's recent work has centered on traveling wave solutions to free boundary problems in fluid dynamics, particularly for the Navier-Stokes equations. His research explores well-posedness, stability, and the behavior of solutions under various conditions including vanishing viscosity and surface tension limits. He has developed novel analytical techniques involving anisotropic Sobolev spaces and Nash-Moser implicit function theorems to address these challenging problems.
Scientific Awards:
- Julius Ashkin Teaching Award (2019)
- NSF CAREER Award
Research Support and Mentoring:
Professor Tice has mentored numerous students and postdocs in the field of partial differential equations. His research has been supported by prestigious grants including the NSF CAREER Award. He has collaborated extensively with researchers including Yan Guo, Noah Stevenson, and others on fundamental problems in fluid dynamics and mathematical physics. His work has appeared in top journals including Archive for Rational Mechanics and Analysis, SIAM Journal on Mathematical Analysis, and Communications on Pure and Applied Mathematics.
Research Environment:
Professor Tice is affiliated with the Center for Nonlinear Analysis at Carnegie Mellon University, which provides a vibrant research environment for the study of nonlinear phenomena in mathematics and its applications. His work contributes to the center's mission of advancing the understanding of nonlinear partial differential equations and their applications to physical problems.
