1. Asymptotic stability of homogeneous solutions of incompressible stationary Navier-Stokes equations
- Author
-
Xukai Yan and Yanyan Li
- Subjects
Unit sphere ,Work (thermodynamics) ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Rotational symmetry ,01 natural sciences ,Physics::Fluid Dynamics ,010101 applied mathematics ,Exponential stability ,Dimension (vector space) ,Stability theory ,Compressibility ,0101 mathematics ,Navier–Stokes equations ,Analysis ,Mathematics - Abstract
It was proved by Karch and Pilarczyk that Landau solutions are asymptotically stable under any L 2 -perturbation. In our earlier work with L. Li, we have classified all ( − 1 ) -homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south and north poles. In this paper, we study the asymptotic stability of the least singular solutions among these solutions other than Landau solutions, and prove that such solutions are asymptotically stable under any L 2 -perturbation.
- Published
- 2021