  We prove the existence of a weak solution to a two-dimensional resonant 3x3
system of conservation laws with BV initial data. Due to possible resonance
(coinciding eigenvalues), spatial BV estimates are in general not available.
Instead, we use an entropy dissipation bound combined with the time translation
invariance property of the system to prove existence based on a two-dimensional
compensated compactness argument adapted from the paper of Tadmor, Rascle and
Bagnerini, "Compensated compactness for 2D conservation laws", [JHDEs
2(3):697--712, 2005]. Existence is proved under the assumption that the flux
functions in the two directions are linearly independent.
