On the Extension of Onsager's Conjecture for General Conservation Laws

The aim of this work is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the "universality" of the Onsager exponent, $\alpha > 1/3$, concerning the regularity of the solutions, say in $C^{0,\alpha}$, that guarantees the conservation of the generalized entropy; regardless of the structure of the genuine nonlinearity in the underlying system.