Onsager’s conjecture in bounded domains for the conservation of entropy and other companion laws

Onsager’s conjecture in bounded domains for the conservation of entropy and other companion laws

We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fractional differentiability of order one-third in the interior of the domain, and if the normal component of the correspondi...

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Veröffentlicht in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2019-10, Vol.475 (2230), p.1-18
Hauptverfasser: Bardos, C., Gwiazda, P., Świerczewska-Gwiazda, A., Titi, E. S., Wiedemann, E.
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container_title Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences
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creator Bardos, C.
Gwiazda, P.
Świerczewska-Gwiazda, A.
Titi, E. S.
Wiedemann, E.
description We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fractional differentiability of order one-third in the interior of the domain, and if the normal component of the corresponding fluxes tend to zero as one approaches the boundary. This extends various recent results of the authors.
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title Onsager’s conjecture in bounded domains for the conservation of entropy and other companion laws
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