On the structure of entropy dissipation and regularity for quasi-entropy solutions to 1d scalar conservation laws and to isentropic Euler system with $γ=3$
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| Format: | Preprint |
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2026
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| _version_ | 1866915712862257152 |
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| author | Ancona, Fabio Marconi, Elio Talamini, Luca |
| author_facet | Ancona, Fabio Marconi, Elio Talamini, Luca |
| contents | 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 $γ= 3$, for which we also slightly improve the available fractional regularity by exploiting the sign of the kinetic measures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_03739 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the structure of entropy dissipation and regularity for quasi-entropy solutions to 1d scalar conservation laws and to isentropic Euler system with $γ=3$ Ancona, Fabio Marconi, Elio Talamini, Luca Analysis of PDEs 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 $γ= 3$, for which we also slightly improve the available fractional regularity by exploiting the sign of the kinetic measures. |
| title | On the structure of entropy dissipation and regularity for quasi-entropy solutions to 1d scalar conservation laws and to isentropic Euler system with $γ=3$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.03739 |