The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place on Wednesday from 9:00 till 10:00 in the room K3. The talk will be given by Alexei Gazca Orozco. Please see the details below.
Speaker: Alexei Gazca Orozco
Title: Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness
Abstract: In this talk, I will present some recent results obtained in collaboration with V. Patel (Oxford) in connection with a system describing an incompressible heat-conducting incompressible fluid. I will introduce the notion of a dissipative weak solution of the system and highlight the connections and differences to the existing approaches in the literature. One of the advantages of the proposed approach is that the solution satisfies a weak-strong uniqueness principle, which guarantees that the weak solution will coincide with the strong solution, as long as the latter exists; moreover, the solutions are constructed via a finite element approximation, leading (almost, not quite) to the first convergence result for the full system including viscous dissipation.