Stochastic and Multiscale Modeling and Computation Seminar by Zhirun Zhan: The Uniqueness of Mild Solutions to the Navier-Stokes Equations in Scale Critical Spaces
Speaker: , Kyoto University.
Title: The Uniqueness of Mild Solutions to the Navier-Stokes Equations in Scale Critical Spaces
Abstract锛歄ur work deals with the uniqueness of mild solutions to the Navier-Stokes equations in the whole space. It is known that the uniqueness of mild solutions to the unforced Navier-Stokes equations holds in $C([0,T];L^d(\mathbb{R}^d))$ when $d\geq3$. As for the forced Navier-Stokes equations, the uniqueness of mild solutions in $C([0,T];L^{d,\infty}(\mathbb{R}^d))$ with force $f$ and initial data $u_{0}$ in appropriate Lorentz spaces is known when $d\geq3$ . We show that for $d\geq3$, the uniqueness of mild solutions to the forced Navier-Stokes equations holds in a wider function space than known scale-critical spaces.
Stochastic and Multiscale Modeling and Computation Seminar