Il primo incontro dei Seminari Volterra si terrà nell'aula riunioni al primo piano dell'Istituto per le Applicazioni del Calcolo, CNR, via dei Taurini 19, 00185 Roma.
Speaker: Michele Coti Zelati (Imperial College London)
Entropy maximization in the two-dimensional Euler equations
We investigate certain questions arising in two-dimensional statistical hydrodynamics, by relying on principles of entropy maximization for the vorticity of a two-dimensional perfect fluid in a disc. In analogy with the entropy functions used in statistical mechanics and thermodynamics, we show that similar concavity properties hold for the 2d Euler equations when maximizing entropies at fixed energy levels. The proofs rely on rearrangement inequalities, a modification of the classical min-max principle, and the properties of the Euler-Lagrange equations for the corresponding constrained optimization.