Sharp and Strong non-uniqueness for the Navier-Stokes equations in R^3.

COLLOQUIUM TALK

Title:  Sharp and Strong non-uniqueness for the Navier-Stokes equations in R^3.
 
Abstract:   In this talk, we prove a sharp and strong non-uniqueness for a class of weak solutions to the incompressible Navier-Stokes equations in $\R^3$. To be more precise, we exhibit the non-uniqueness result in a strong sense, that is, any weak solution  is non-unique in $ L^p([0,T];L^\infty(\R^3))$ with $1\le p<2$, which  is sharp with regard to the classical Ladyzhenskaya-Prodi-Serrin criteria at endpoint $(2, \infty)$, and extends the sharp nonuniqueness for the Navier-Stokes equations on torus $\TTT^3$ in  the  recent groundbreaking work (Cheskidov and Luo, Invent. Math., 229 (2022), pp. 987-1054) to the setting of the whole space. The key ingredient is developing a new iterative scheme that balances the compact support of the Reynolds stress error with the non-compact support of the solution via introducing  incompressible perturbation fluid. This work is joint with Changxing Miao and Weikui Ye.

Venue: ONLINE (details below)

Join Zoom Meeting
https://zoom.us/j/97443614179?pwd=d3V1SXViR1NoVUtNUTd1N1p4WVF3UT09

Meeting ID: 974 4361 4179
Passcode: 855648