Seminar on partial differential equations

Wild solutions for isentropic Euler equations starting from smooth initial data

In a series of papers starting with the groundbreaking work of De Lellis and Székelyhidi several authors have shown that there might exist infinitely many bounded weak solutions to the isentropic Euler equations satisfying the energy inequality and starting from certain class of initial data. Concerning smoothness, the best result is due to Chiodaroli, De Lellis and Kreml, where the existence of these wild solutions was shown for Lipschitz initial data. In this talk we present the same result for smooth initial data. The proof is based on a nontrivial generalization of the previous theorem, in particular on a notion of generalized fan subsolution.
This is a joint work with E. Chiodaroli, V. Mácha and S. Schwarzacher.