19 citations · 118 across the 38 of their papers we have counts for
39 papers
Long-Wave Stability And Instability Of Periodic Shear Flows For The 2D Navier-Stokes Equations On The -Plane
Robin Ming Chen, Tian Dai, Dehua Wang +1
We study the spectral stability of periodic shear flows for the two-dimensional Navier--Stokes equations on the -plane in the long-wave regime. While it is known that non-rotati…
On Serrin Interior Regularity Criterion for Navier-Stokes Equations
Robin Ming Chen, Giovanni P. Galdi, Bruno Poggi +1
We revisit Serrin's interior spatial regularity criterion for distributional solutions to the Navier-Stokes equations in and considerably relax the hypotheses in two…
Asymptotic stability of smooth solitons and multi-solitons for the Camassa--Holm equation
Robin Ming Chen, Yang Lan, Yue Liu +1
We establish the asymptotic stability of smooth solitons and multi-solitons for the Camassa-Holm (CH) equation in the energy space . We show that solutions initially close…
Extreme internal waves: gravity currents and overturning fronts
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
Hydrodynamic bores are front-type traveling wave solutions to the two-layer free boundary Euler equations in two dimensions. The velocity field in each layer is assumed to be incom…
Finite-time self-similar implosion of hollow vortices
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this paper, we consider the finite-time blowup of hollow vortices. These are solutions of the two-dimensional Euler equations for which the fluid domain is the complement of fin…
Nonlinear stability of compressible vortex sheets in three-dimensional elastodynamics
Robin Ming Chen, Feimin Huang, Dehua Wang +1
We investigate the nonlinear stability of compressible vortex sheet solutions for three-dimensional (3D) isentropic elastic flows. Building upon previous results on the weakly line…
Vortex-carrying solitary gravity waves of large amplitude
Robin Ming Chen, Kristoffer Varholm, Samuel Walsh +1
In this paper, we study two-dimensional traveling waves in finite-depth water that are acted upon solely by gravity. We prove that, for any supercritical Froude number (non-dimensi…
Higher Order Gauge Equivariant CNNs on Riemannian Manifolds and Applications
Gianfranco Cortes, Yue Yu, Robin Chen +3
With the advent of group equivariant convolutions in deep networks literature, spherical CNNs with -equivariant layers have been developed to cope with data that ar…
Desingularization and global continuation for hollow vortices
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
A hollow vortex is a region of constant pressure bounded by a vortex sheet and suspended inside a perfect fluid; it can therefore be interpreted as a spinning bubble of air in wate…
Rigidity of three-dimensional internal waves with constant vorticity
Robin Ming Chen, Lili Fan, Samuel Walsh +1
This paper studies the structural implications of constant vorticity for steady three-dimensional internal water waves. It is known that in many physical regimes, water waves benea…
Transverse instability of the CH-KP-I equation
Robin Ming Chen, Jie Jin
The Camassa-Holm-Kadomtsev-Petviashvili-I equation (CH-KP-I) is a two dimensional generalization of the Camassa-Holm equation (CH). In this paper, we prove transverse instability o…
Global ill-posedness for a dense set of initial data to the Isentropic system of gas dynamics
Robin Ming Chen, Alexis F. Vasseur, Cheng Yu
In dimension and , we show that for any initial datum belonging to a dense subset of the energy space, there exist infinitely many global-in-time admissible weak solutions…
Global bifurcation of solitary waves to the Boussinesq system
Robin Ming Chen, Jie Jin
The Boussinesq system arises in the modeling of long wave small amplitude water waves in a channel, where the four parameters satisfy one constraint. In this pap…
Orbital stability of internal waves
Robin Ming Chen, Samuel Walsh
This paper studies the nonlinear stability of capillary-gravity waves propagating along the interface dividing two immiscible fluid layers of finite depth. The motion in both regio…
Global bifurcation of anti-plane shear fronts
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
We consider anti-plane shear deformations of an incompressible elastic solid whose reference configuration is an infinite cylinder with a cross section that is unbounded in one dir…
Large-amplitude internal fronts in two-fluid systems
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this announcement, we report results on the existence of families of large-amplitude internal hydrodynamic bores. These are traveling front solutions of the full two-phase incom…
A Kato-type criterion for vanishing viscosity near the Onsager's critical regularity
Robin Ming Chen, Zhilei Liang, Dehua Wang
We consider a vanishing viscosity sequence of weak solutions of the three-dimensional Navier--Stokes equations on a bounded domain. In a seminal paper [25] Kato showed that for suf…
Global bifurcation for monotone fronts of elliptic equations
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this paper, we present two results on global continuation of monotone front-type solutions to elliptic PDEs posed on infinite cylinders. This is done under quite general assumpt…
instability of -stable peakons in the Novikov equation
Robin Ming Chen, Dmitry E. Pelinovsky
It is known from the previous works that the peakon solutions of the Novikov equation are orbitally and asymptotically stable in . We prove, via the method of characteristics,…
Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this paper, we present a novel center manifold reduction theorem for quasilinear elliptic equations posed on infinite cylinders. This is done without a phase space in the sense…
Analysis of variable-step/non-autonomous artificial compression methods
Robin Ming Chen, William Layton, Michael McLaughlin
A standard artificial compression (AC) method for incompressible flow is $$ \frac{u_{n+1}^{\varepsilon }-u_{n}^{\varepsilon }}{k}+u_{n+1}^{\varepsilon }\cdot \nabla u_{n+1}^{\varep…
Gaussian Behavior in Zeckendorf Decompositions From Lattices
Eric Chen, Robin Chen, Lucy Guo +4
Zeckendorf's Theorem states that any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers. We consider higher-dimensional lattice analogues, where a…
Linear Stability of Compressible Vortex Sheets in 2D Elastodynamics: Variable Coefficients
Robin Ming Chen, Jilong Hu, Dehua Wang
The linear stability with variable coefficients of the vortex sheets for the two-dimensional compressible elastic flows is studied. As in our earlier work on the linear stability w…
Martingale solutions for the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by Levy processes
Robin Ming Chen, Dehua Wang, Huaqiao Wang
In this paper, the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by Lévy process consisting of the Brownian motion, the compensated Pois…