Jeaheang Bang : Self-Similar Solutions to the Stationary Navier-Stokes Equations in a Higher Dimensional Cone

Posted by Christof Sparber , part of the Analysis and Applied Mathematics Seminar.

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Feb. 17, 2025, 4 p.m.

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Abstract

Self-similar solutions play an important role in understanding the regularity and asymptotic behavior of solutions to the Navier-Stokes equations. We recently showed that axisymmetric self-similar solutions to the stationary Navier-Stokes equations in an $n$-dimensional cone with the no-slip boundary condition except at the origin must be trivial when $n\geq 4$. It rules out this particular scenario of boundary singularity, which has finite Dirichlet energy when $n\geq 5$. The main idea is to apply ODE techniques along with a sign property of the head pressure. This is a joint work with Changfeng Gui, Hao Liu, Yun Wang and Chunjing Xie.