49 citations · 140 across the 13 of their papers we have counts for
5 papers · 1 filter
Para-differential Calculus on Compact Lie Groups and Spherical Capillary Water Waves
Chengyang Shao
This paper provides a para-differential calculus toolbox on compact Lie groups and homogeneous spaces. It helps to understand non-local, nonlinear partial differential operators wi…
Longtime Dynamics of Irrotational Spherical Water Drops: Initial Notes
Chengyang Shao
In this note, we propose several unsolved problems concerning the irrotational oscillation of a water droplet under zero gravity. We will derive the governing equation of this phys…
Strichartz and Multi-linear Estimates for the One-dimensional Periodic Dysthe equation
Garrett Heller, Chengyang Shao
This paper presents Strichartz estimates for the linearized 1D periodic Dysthe equation on the torus, namely estimate of the norm of the solution in terms…
Long Time Behavior of a Quasilinear Hyperbolic System Modelling Elastic Membranes
Chengyang Shao
The paper studies the long time behavior of a system that describes the motion of a piece of elastic membrane driven by surface tension and inner air pressure. The system is a dege…
Schauder Type Estimates for a Class of Hypoelliptic Operators
Chengyang Shao
The present paper aims to generalize the Schauder estimate for a class of higher-order hypo-elliptic operators. The results in the present paper apply to parabolic equations of hig…