F. Ancona - E. Marconi - L. Talamini
On the structure of entropy dissipation and regularity for quasi-entropy solutions to 1d scalar conservation laws and to isentropic Euler system with $\gamma=3$
Preprint
Inserted: 7 jan 2026
Last Updated: 7 jan 2026
Year: 2026
Abstract:
In this paper, we first investigate quasi-entropy solutions to scalar conservation laws in several space dimensions. In this setting, we introduce a suitable Lagrangian representation for such solutions. Next, we prove that, in one space dimension and for fluxes $f$ satisfying a general non-degeneracy condition, the entropy dissipation measures of quasi-entropy solutions are concentrated on a $1$-rectifiable set. The same result is obtained for the isentropic Euler system with $\gamma = 3$, for which we also slightly improve the available fractional regularity by exploiting the sign of the kinetic measures.
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