Abstract
Inspired by an open question by Chemin, Zhang and Zhang about the regularity of the 3D Navier–Stokes equations with one initially small component, we investigate symmetry breaking and symmetry preservation. Our results fall in three classes. First we prove strong symmetry breaking. Specifically, we demonstrate third component norm inflation (3rdNI) and Isotropic Norm Inflation (INI) starting from zero third component. Second we prove symmetry breaking for initially zero third component, even in the presence of a favorable initial pressure gradient. Third we study certain symmetry preserving solutions with a shear flow structure. Specifically, we give applications to the inviscid limit and exhibit explicit solutions that inviscidly damp to the Kolmogorov flow.
| Original language | English |
|---|---|
| Article number | 25 |
| Journal | Communications in Mathematical Physics |
| Volume | 405 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 31 Jan 2024 |
Funding
CP and JT are partially supported by the Agence Nationale de la Recherche, project BORDS, grant ANR-16-CE40-0027-01. CP is also partially supported by the Agence Nationale de la Recherche, project SINGFLOWS, grant ANR- 18-CE40-0027-01, project CRISIS, grant ANR-20-CE40-0020-01, by the CY Initiative of Excellence, project CYNA (CY Nonlinear Analysis) and project CYFI (CYngular Fluids and Interfaces). JT is also supported by the Labex MME-DII. TB and CP thank the Institute of Advanced Studies of Cergy Paris University for their hospitality.
| Funders | Funder number |
|---|---|
| Institute of Advanced Studies of Cergy Paris University | |
| French National Research Agency | ANR-20-CE40-0020-01, ANR- 18-CE40-0027-01, ANR-16-CE40-0027-01 |
| Labex Immuno-Oncology |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics