44 citations · 312 across the 44 of their papers we have counts for
14 papers · 1 filter
Remarks on the Rayleigh-Benard Convection on Spherical Shells
Shouhong Wang, Ping Yang
The main objective of this article is to study the effect of spherical geometry on dynamic transitions and pattern formation for the Rayleigh-Benard convection. The study is mainly…
Dynamic Transitions of Surface Tension Driven Convection
Henk Dijkstra, Taylan Sengul, Shouhong Wang
We study the well-posedness and dynamic transitions of the surface tension driven convection in a three-dimensional (3D) rectangular box with non-deformable upper surface and with…
Pattern Formation and Dynamic Transition for Magnetohydrodynamic Convection
Taylan Sengul, Shouhong Wang
The main objective of this paper is to describe the dynamic transition of the incompressible MHD equations in a three dimensional (3D) rectangular domain from a perspective of patt…
Dynamic Transitions for Quasilinear Systems and Cahn-Hilliard equation with Onsager mobility
Honghu Liu, Taylan Sengul, Shouhong Wang
The main objectives of this article are two-fold. First, we study the effect of the nonlinear Onsager mobility on the phase transition and on the well-posedness of the Cahn-Hilliar…
Phase Transitions for the Brusselator Model
Tian Ma, Shouhong Wang
Dynamic phase transitions of the Brusselator model is carefully analyzed, leading to a rigorous characterization of the types and structure of the phase transitions of the model fr…
Phase Transitions for Belousov-Zhabotinsky Reactions
Tian Ma, Shouhong Wang
The main objective of this article is to study the dynamic phase transitions associated with the spatial-temporal oscillations of the BZ reactions, given by Field, Koros and Noyes,…
Dynamic Transition and Pattern Formation in Taylor Problem
Tian Ma, Shouhong Wang
The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, using the dynamic transition theory and geometric theory of incom…
Tropical Atmospheric Circulations: Dynamic Stability and Transitions
Tian Ma, Shouhong Wang
In this article, we present a mathematical theory of the Walker circulation of the large-scale atmosphere over the tropics. This study leads to a new metastable state oscillation t…
Cahn-Hilliard Equations and Phase Transition Dynamics for Binary Systems
Tian Ma, Shouhong Wang
The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase tr…
Dynamic Phase Transitions in PVT Systems
Tian Ma, Shouhong Wang
The main objective of this article are two-fold. First, we introduce some general principles on phase transition dynamics, including a new dynamic transition classification scheme,…
Some Mathematical and Numerical Issues in Geophysical Fluid Dynamics and Climate Dynamics
Jianping Li, Shouhong Wang
In this article, we address both recent advances and open questions in some mathematical and computational issues in geophysical fluid dynamics (GFD) and climate dynamics. The main…
Addendum to the paper "Two-Dimensional Infinite Prandtl Number Convection: Structure of Bifurcated Solutions, J. Nonlinear Sci., 17(3), 199-220, 2007"
Tian Ma, Jungho Park, Shouhong Wang
The main objective of this addendum to the mentioned article by Park is to provide some remarks on bifurcation theories for nonlinear partial differential equations (PDE) and their…
Boundary-Layer and Interior Separations in the Taylor--Couette--Poiseuille Flow
Tian Ma, Shouhong Wang
In this article, we derive a rigorous characterization of the boundary-layer and interior separations in the Taylor-Couette-Poiseuille (TCP) flow. The results obtained provide a ri…
Stratified Rotating Boussinesq Equations in Geophysical Fluid Dynamics: Dynamic Bifurcation and Periodic Solutions
Chun-Hsiung Hsia, Tian Ma, Shouhong Wang
The main objective of this article is to study the dynamics of the stratified rotating Boussinesq equations, which are a basic model in geophysical fluid dynamics. First, for the c…