Large self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field

Lorenzo Brandolese (1, 2, 3) , Grzegorz Karch (4)

1 UCBL - Université Claude Bernard Lyon 1
2 ICJ - Institut Camille Jordan
3 EDPA - Équations aux dérivées partielles, analyse
4 Uniwersytet Wroclawski = University of Wroclaw

The Navier-Stokes system for an incompressible fluid coupled with the equation for a heat transfer is considered in the whole three dimensional space. This system is invariant under a suitable scaling. Using the Leray-Schauder theorem and compactness arguments, we construct self-similar solutions to this system without any smallness assumptions imposed on homogeneous initial conditions.

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brandolese, Grzegorz Karch. Large self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field. 2023. ⟨hal-04267591⟩