Well posedness of the Euler system of gas dynamics

Abstract: We discuss the well posedness of the Euler system of gas dynamics from two different perpectives: 1. Admissible solutions are inviscid limits of the Navier-Stokes-Fourier system. 2. Admissible solutions comply with the maximum entropy production principle. We show that these two criteria are in general not compatible and give rise to different classes of solutions.

Then we propose and admissibility criterion that gives rise to a unique solution semigroup of the Euler system in the class of generalized dissipative solutions. The solutions are Borel measurable meaning ``almost'' continuous with respect to the initial data.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)