GT des doctorants ANH et ANEDP
The fractional Navier-Stokes-Boussinesq system and the choice of initial data
24
mars 2026
mars 2026
| Intervenant : | Maxence Mansais |
| Institution : | LAMME |
| Heure : | 10h30 - 11h30 |
| Lieu : | 2L8 |
In this talk I will discuss the construction of global in time Mild solutions to the fractional Navier-Stokes-Boussinesq system (same fractional dissipation on the velocity and on the temperature) on the entire space in a critical setting for small initial data.
While a maximal critical space of resolution for the initial velocity is well known for the fractional Navier-Stokes system, obstacles exist to find the largest possible critical spaces of resolution simultaneously for the initial velocity, initial temperature and external force.
As an illustration of these obstacles, I will discuss and compare the framework of parabolic Morrey spaces applied to the fractional Navier-Stokes and to the fractional Navier-Stokes-Boussinesq system. Recent developments about other frameworks allowing for a trade-off in the choice of the regularity between initial velocity and initial temperature will also be presented.