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Rigidity for homogeneous solutions to the two-dimensional Euler equations in sector-type domains
Li Li, Xukai Yan, Zhibo Yang
We study the rigidity problem for -homogeneous solutions to the two-dimensional incompressible stationary Euler equations in sector-type domains $Ω_{a, b, θ_0}:= \{(r,θ): a<r…
Recent research on -homogeneous solutions of stationary Navier-Stokes equations
Li Li, Xukai Yan
We make an exposition of recent research on -homogeneous solutions of the three-dimensional incompressible stationary Navier-Stokes equations with singular rays. We also disc…
Removable singularity of (-1)-homogeneous solutions of stationary Navier-Stokes equations
Li Li, YanYan Li, Xukai Yan
We study the removable singularity problem for -homogeneous solutions of the three-dimensional incompressible stationary Navier-Stokes equations with singular rays. We prove…
Sharp stability for the interaction energy
Xukai Yan, Yao Yao
This paper is devoted to stability estimates for the interaction energy with strictly radially decreasing interaction potentials, such as the Coulomb and Riesz potentials. For a ge…
Asymptotic stability of homogeneous solutions of incompressible stationary Navier-Stokes equations
Yan Yan Li, Xukai Yan
It was proved by Karch and Pilarzyc that Landau solutions are asymptotically stable under any -perturbation. In our earlier work with L. Li, we have classified all -homo…
Uniqueness and non-uniqueness of steady states of aggregation-diffusion equations
Matias G. Delgadino, Xukai Yan, Yao Yao
We consider a nonlocal aggregation equation with degenerate diffusion, which describes the mean-field limit of interacting particles driven by nonlocal interactions and localized r…