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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.

MSC:

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