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

ABSTRACT: 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.

SUBMITTER: Bardos C

PROVIDER: S-EPMC6834034 | biostudies-literature | 2019 Oct

REPOSITORIES: biostudies-literature

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

Bardos C C Gwiazda P P Świerczewska-Gwiazda A A Titi E S ES Wiedemann E E

Proceedings. Mathematical, physical, and engineering sciences 20191016 2230

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. ...[more]

PMID: 31736643

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