6 papers · 1 filter
Inviscid damping without derivatives near Couette flow
Dengjun Guo, Xiaoyutao Luo
We study the long-time dynamics near Couette flow for the 2D Euler equations in unbounded geometries. We identify a mechanism of nonlinear inviscid damping at Yudovich regularity,…
Flexibility and rigidity for the Couette flow in the infinite channel
Dengjun Guo, Xiaoyutao Luo, Guolin Qin
We investigate the existence of stationary and traveling wave solutions to the 2D Euler equations near the Couette flow in the infinite channel . For Sobo…
Asymptotic stability of shear flows for 2D Euler equations at Yudovich regularity
Dengjun Guo, Xiaoyutao Luo
The nonlinear asymptotic stability of shear flows in the 2D Euler equations has traditionally been linked to inviscid damping in the periodic setting. Since Gevrey regularity is re…
Global dynamics of a single vortex ring
Dengjun Guo, In-Jee Jeong, Lifeng Zhao
We study the global-in-time dynamics of vortex rings for the three-dimensional incompressible Euler equations, under the assumption of axisymmetric flows without swirl. For a broad…
Norm Inflation For The Critical SQG Equation
Dengjun Guo, Xiaoyutao Luo
We consider the critical dissipative surface quasi-geostrophic (SQG) equation on or . Despite global regularity of the equation, we show that the data-…
Long time inviscid damping near Couette in Sobolev spaces
Dengjun Guo, Xiaoyutao Luo
We give an elementary proof of long time inviscid damping for Sobolev perturbations near the Couette flow for the 2D Euler equations on . For…