DATE: February 12, 2019 ONSAGER’S CONJECTURE IN BOUNDED DOMAINS FOR THE CONSERVATION OF ENTROPY AND OTHER COMPANION LAWS

摘要: 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 1/3 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.