Forward Discretely Self-Similar Solutions of the 3D Incompressible Navier-Stokes Equations


Tai-Peng Tsai

14:10:00 - 15:00:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Extending the work of Jia and Sverak on self-similar solutions of the Navier-Stokes equations, we show the existence of large, forward, discretely self-similar (DSS) solutions for DSS initial data $u_0$ with factor $\lambda$, assuming either the DSS factor $\lambda$ is sufficiently close to 1 according to the Holder norm of $u_0$, or if $u_0$ is axisymmetric with no swirl. I will also discuss their relevance to the uniqueness problem, and my joint work with D. Chae on the corresponding existence problem of DSS solutions for Euler equations.

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