On the extension of Onsager’s conjecture for general conservation laws. (English) Zbl 1420.35202

Summary: 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.


35Q31 Euler equations
35B33 Critical exponents in context of PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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