Research Interests:

Mathematical analysis and simulation of models for free boundary problems and problems in biomechanics and environmental sciences. My research focuses on free boundary problems arising in a variety of physical contexts ranging from fluid mechanics to solidification such as Hele-Shaw flow, dendritic growth and tumor growth.

Selected Publications:

• X. Xie, Nonexistence of Steady Saffman-Taylor Fingers by Kinetic Undercooling, International Journal of Evolution Equations Volume 10, Number 1 (2016) pp. 75-99. 
• X. Xie, Discrete point spectrum of linear stability operator for Saffman-Taylor bubbles with nonzero surface tension, J. Math. Anal. Appl. 441 (2016) 612-623.
• X. Xie, Some rigorous results in linear stability of steady needle crystals, International Journal of Evolution Equations, Volume 9, Number 1 (2014) pp. 137-150.
• S. Tanveer, X. Xie; Analyticity and nonexistence of classical steady Hele-Shaw fingers, Communications on pure and applied mathematics, Vol. 56, no 3, 353-402 (2003).
• X. Xie, S. Tanveer, Rigorous Results in Steady Finger selection in Viscous Fingering, Archive for rational mechanics and analysis, 166 (2003) 3, 219-286.