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math.AP2025
The Rayleigh-Taylor instability with local energy dissipation
Björn Gebhard, József J. Kolumbán
We consider the inhomogeneous incompressible Euler equations including their local energy inequality as a differential inclusion. Providing a corresponding convex integration theor…
math.AP2024
Entropy solutions to macroscopic IPM
Ãngel Castro, Daniel Faraco, Björn Gebhard
We investigate maximal potential energy dissipation as a selection criterion for subsolutions (coarse grained solutions) in the setting of the unstable Muskat problem. We show that…
math.AP2024
On the energy-constrained optimal mixing problem for one-dimensional initial configurations
Björn Gebhard
We consider the problem of mixing a passive scalar in a periodic box by incompressible vector fields subject to a fixed energy constraint. In that setting a lower bound for the tim…