6 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. It is known that non-rotating per…
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…
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…
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…