# Ian Tice

## Associate Professor

**Address:**

6206 Wean Hall

Department of Mathematical Sciences

Carnegie Mellon University

5000 Forbes Avenue

Pittsburgh, PA 15213

**P:** 412-268-2549

# Education

Ph.D. in Mathematics, Courant Institute, New York University

Postdoctoral Appointments:

- Université Paris-Est Créteil, Laboratoire d'Analyse et de Mathématiques Appliquées
- Brown University, Division of Applied Mathematics

# Awards

- Julius Ashkin Teaching Award, 2019
- NSF CAREER Award

# Research

The focus of my research is the analysis of nonlinear partial differential equations. Although I am broadly interested in the subject, my work has concentrated on those equations arising in physics, and in particular those coming from interfacial fluid mechanics and the Ginzburg-Landau model of superconductivity. In both cases my work focuses on the behavior of certain types of singularities in the physical systems that present many serious challenges in the analysis of the equations. For fluids these singularities are surfaces of discontinuity across which the fluid properties change drastically, while for superconductors they are point singularities known as vortices.

# Select Publications

Y. Guo, I. Tice. (2018). Stability of contact lines in fluids: 2D Stokes Flow. *Arch. Ration. Mech. Anal.* **227** (2), 767-854.

C. Kim, I. Tice. (2017). Dynamics and stability of surfactant-driven surface waves. *SIAM J. Math. Anal.* **49** (2), 1295-1332.

J. Jang, I. Tice, Y. J. Wang. (2016). The compressible viscous surface-internal wave problem: stability and vanishing surface tension limit. *Comm. Math. Phys.* **343** (3), 1039-1113.

Y. Guo, I. Tice. (2013). Almost exponential decay of periodic viscous surface waves without surface tension. *Arch. Rational Mech. Anal.* **207** (2), 459-531.

Y. Guo, I. Tice. (2013). Decay of viscous surface waves without surface tension in horizontally infinite domains. *Anal. PDE,* **6** (6), 1429-1533.

S. Serfaty, I. Tice. (2011). Ginzburg-Landau vortex dynamics with pinning and strong applied currents. *Arch. Rational Mech. Anal.* **201** (2), 413-464.

I. Tice. (2010). Ginzburg-Landau vortex dynamics driven by an applied boundary current. *Comm. Pure Appl. Math.* **63** (12), 1622-1676.