16 citations · 21 across the 13 of their papers we have counts for
13 papers
Classification of local -homogeneous axisymmetric solutions of the D stationary Navier-Stokes equations with logarithmic singular-ray behavior
Xukai Yan
We study the existence and classification of local -homogeneous axisymmetric solutions of the three-dimensional incompressible stationary Navier-Stokes equations nea…
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…
Anisotropic Caffarelli-Kohn-Nirenberg type inequalities
YanYan Li, Xukai Yan
Caffarelli, Kohn and Nirenberg considered in 1984 the interpolation inequalities \[\||x|^{γ_1}u\|_{L^s(\mathbb{R}^n)}\le C\||x|^{γ_2}\nabla u\|_{L^p(\mathbb{R}^n)}^a\||x|^{γ_3}u\|_…
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…
Symmetry of hypersurfaces with ordered mean curvature in one direction
Yanyan Li, Xukai Yan, Yao Yao
For a connected -dimensional compact smooth hypersurface without boundary embedded in , a classical result of Aleksandrov shows that it must be a sphere if…
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…
Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. III. Two singularities
Li Li, YanYan Li, Xukai Yan
All -homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus north and s…
Vanishing viscosity limit for homogeneous axisymmetric no-swirl solutions of stationary Navier-Stokes equations
Li Li, Yan Yan Li, Xukai Yan
-homogeneous axisymmetric no-swirl solutions of three dimensional incompressible stationary Navier-Stokes equations which are smooth on the unit sphere minus the north and so…
Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. II. Classification of axisymmetric no-swirl solutions
Li Li, YanYan Li, Xukai Yan
We classify all (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus t…
Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. I. One singularity
Li Li, YanYan Li, Xukai Yan
We classify all homogeneous axisymmetric no swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus…