The Rayleigh-B\'enard convection problem deals with the motion of a compressible fluid in a tunnel heated from below and cooled from above. In this context, the so-called Boussinesq relation is used, claiming that the density deviation from a constant reference value is a linear function of the temperature. These density and temperature deviations then satisfy the so-called Oberbeck-Boussinesq equations. The rigorous derivation of this system from the full compressible Navier-Stokes-Fourier system was done by Feireisl and Novotn\'y for conservative boundary conditions on the fluid's velocity and temperature. In this talk, we investigate the derivation for Dirichlet boundary conditions, and show that differently to the case of conservative boundary conditions, the limiting system contains an unexpected non-local temperature term. This is joint work with Peter Bella (TU Dortmund) and Eduard Feireisl (CAS).
Seminar on Partial Differential Equations
usually takes place each Tuesday at 09:00 in IM, rear building, ground floorChair: Šárka Nečasová, Milan Pokorný
An unexpected term for the Oberbeck--Boussinesq approximation
Florian Oschmann
Institute of Mathematics, CAS
Tuesday, 4. October 2022 - 9:00 to 10:00
Global existence of weak solutions in nonlinear 3D thermoelasticity
Srđan Trifunović
University of Novi Sad
Tuesday, 14. June 2022 - 9:00 to 10:00
See the attached file.
On deterministic and stochastic obstacle problems
Yassine Tahraoui
NOVA University Lisbon
Tuesday, 31. May 2022 - 9:00 to 10:00
See the attached file.
Uniform boundary stabilization of the 3D- Navier-Stokes Equations and of 2D and 3D Boussinesq system by Finite dimensional localized boundary feedback controllers in Besov spaces of low regularity
Buddhika Priyasad
Charles University
Wednesday, 18. May 2022 - 10:15 to 11:15
In this talk, I present two stabilization problems of fluid equations, namely the Navier-Stokes Equations and the Boussinesq System, both in d = 2,3 setting. For the Navier Stokes problem, we use two localized controls {v, u} where the boundary control v localized on a small portion of the boundary and the interior control u localized on an arbitrarily small collar supported on the same boundary portion. For the Boussinesq problem, we use two localized controls {v, u} where v acting on the thermal equation as a localized boundary control and u acting as a localized interior control for the fluid equation. The initial conditions for both systems are taken of low regularity. We then seek to uniformly stabilize both systems in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of an explicitly constructed, finite-dimensional feedback control pair {v, u}.... more