Oberseminar Mathematical Fluid Dynamics

A famous conjecture by Onsager relates the regularity of a weak solution of the incompressible Euler equations
to energy conservation. This conjecture has been proven in recent years. In this talk we study the hydrostatic
incompressible Euler equations, which describe e.g. the dynamics of the ocean. We present some recent results
on our attempt to establish a relation between regularity and energy conservation for these equations, similar
to Onsager’s conjecture. In this context we discuss different notions of weak solutions. This talk is based on
joint work with Daniel W. Boutros and Edriss S. Titi.