On the existence and compactness of a two-dimensional resonant system of conservation laws

Details On the existence and compactness of a two-dimensional resonant system of conservation laws On the existence and compactness of a two-dimensional resonant system of conservation laws

2006-10-03

arxiv.org/abs/math/0610099v2

Mathematics

Analysis of PDEs

Scientific paper

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.

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