## Research Unit Seminar Dec 12, 2023

**Speaker:**Daniel Boutros (University of Cambridge) 16h00, Stefan Dingel (Universität Kassel) 17h00 (cancelled)**Date:**Dec 12, 2023 16h00 - 18h00**Location:**Room 315 (Schlossgartenstraße 7 (S2|15), 64289 Darmstadt) and online**Abstracts:**

## "On energy conservation for inviscid hydrodynamic equations: analogues of Onsager's conjecture"

Onsager's conjecture states that 1/3 is the critical spatial (Hölder) regularity threshold for energy conservation by weak solutions of the incompressible Euler equations. We consider an analogue of Onsager's conjecture for the inviscid primitive equations of oceanic and atmospheric dynamics. The anisotropic nature of these equations allows us to introduce new types of weak solutions and prove a range of independent sufficient criteria for energy conservation. Therefore there probably is a 'family' of Onsager conjectures for these equations.

Furthermore, we employ the method of convex integration to show the nonuniqueness of weak solutions to the inviscid and viscous primitive equations (and also the Prandtl equations), and to construct examples of solutions that do not conserve energy in the inviscid case. Finally, we present a regularity result for the pressure in the Euler equations, which is of relevance to the Onsager conjecture in the presence of physical boundaries. As an essential part of the proof, we introduce a new weaker notion of pressure boundary condition which we show to be necessary by means of an explicit example. These results are joint works with Claude Bardos, Simon Markfelder and Edriss S. Titi.

## "On existence of global weak solutions to Hibler’s sea-ice model" (cancelled)

Our aim is to show the existence of global solutions to the sea ice model first published by W.D. Hilber in 1979. In this talk, we discuss some challenges and work-arounds and a general strategy of proof based on the construction of Lions-type solutions for the compressible Navier-Stokes equations.