On stability of weak Navier–Stokes solutions with large L<sup>3,∞</sup>initial data

Author: 

Barker, T
Seregin, G
Šverák, V

Publication Date: 

1 May 2018

Journal: 

Communications in Partial Differential Equations

Last Updated: 

2020-07-19T18:37:20.26+01:00

DOI: 

10.1080/03605302.2018.1449219

page: 

1-24

abstract: 

© 2018 Taylor & Francis We consider the Cauchy problem for the Navier–Stokes equation in ℝ3×]0,∞[ with the initial datum (Formula presented.), a critical space containing nontrivial (−1)−homogeneous fields. For small (Formula presented.) one can get global well-posedness by perturbation theory. When (Formula presented.) is not small, the perturbation theory no longer applies and, very likely, the local-in-time well-posedness and uniqueness fails. One can still develop a good theory of weak solutions with the following stability property: If u(n)are weak solutions corresponding the the initial datum (Formula presented.), and (Formula presented.) converge weakly* in (Formula presented.) to u0, then a suitable subsequence of u(n)converges to a weak solution u corresponding to the initial condition u0. This is of interest even in the special case u0≡0.

Symplectic id: 

853764

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article