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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, α> 1 / 3 , concerning the regularity of the solutions, say in C ,α , that guarantees the conservation of the generalized entropy, regardless of the structure of the genuine nonlinearity in the underlying system.

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