My mathematical research is in the area of dynamics of PDEs, particularly those arising from fluid mechanics. My recent completed work focuses on the instability and inviscid damping of two dimensional water wave problems.
Publication List
[1] Capillary gravity water waves linearized at monotone shear flows: eigenvalues and inviscid damping, 94 pages, Submitted, http://arxiv.org/abs/2110.12604. (With C. Zeng.)
[2] Linear instability of two-phase fluids interface problem, Submitted, http://arxiv.org/abs/2208.
[3] Linearized gravity water waves at monotone shear flows, In preparation. (With C. Zeng.)
Talks
[1] Analysis of Linearized Capillary Gravity Water Waves near Monotone Shear Flow, Special session on ”Geometric methods in spectral stability of waves and patterns” at The Twelfth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Athens, GA (March 29, 2022)
[2] Capillary Gravity Water Waves Linearized at Monotone Shear Flows: Eigenvalues and Inviscid Damping, AMI Seminar, University of Alberta, Virtual (January 28, 2022)
[3] 2D Incompressible Euler Equation Linearized at Shear Flows: An Introduction, AMI Seminar, University of Alberta, Virtual (January 21, 2022)
[4] Linear Instability in Fluid Free Surface Problems, Graduate Student Working Group, MSRI, May 12th 2021. https://www.msri.org/seminars/25835