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tice
Ian Tice, Assistant Professor
Ph.D., Courant Institute, New York University
E-mail: iantice@andrew.cmu.edu
Office: Wean Hall 7206
Phone: 412-268-7583
Personal web site

Research:

Broadly speaking, my research interests include nonlinear partial differential equations and the calculus of variations, as well as their applications in in physics and materials science.  My work has focused on two distinct areas: stability analysis in interfacial fluid mechanics, and analysis of vortices in the Ginzburg-Landau model of superconductivity.

In the area of fluid mechanics, I study the well-posedness (existence and uniqueness of solutions, and their dependence on the data of the problem), stability (both orbital and asymptotic), and parameter asymptotics of various models of fluid mechanics involving a sharp interface between two immiscible fluids.  For example, I have proved results on the global well-posedness and decay of the viscous surface wave problem and the viscous surface-internal wave problem, the linear and nonlinear Rayleigh-Taylor instability of compressible fluids, and the instability of gaseous stars.  In the context of the Ginzburg-Landau model, I am interested in understanding the dynamics and energetics of superconducting vortices, point-like defects that appear in superconducting materials.  I derived the vortex dynamics in superconductors driven by electric currents, inhomogeneous magnetic fields, and material defect pinning; I also worked on Lorentz space estimates for the Ginzburg-Landau free energy and the Coulombian renormalized energy.