Finer representation of the Jaumann defect

Derive a finer representation of the Jaumann defect that distinguishes oscillation from concentration, for example through a Young-measure or microlocal measure description, and characterizes the directions of interaction between the deviatoric strain and the velocity-gradient vorticity.

Background

The paper identifies the defect only as an element of $L^2(0,T;(H^2(\Omega;S_0))^*)$, a space determined by an $L^2(0,T;L^1(\Omega))$ bound on the Jaumann commutator. This level of information records the size of the defect but not the mechanism producing it.

The authors suggest that Young measures could separate oscillation from concentration, while H-measures could additionally describe the directions in which the deviatoric strain and vorticity factors oscillate against each other. No such representation is obtained in the paper.