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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2022

Entropy solutions in $BV^s$ for a class of triangular systems involving a transport equation

Résumé

In this article, we consider a class of strictly hyperbolic triangular systems involving a transport equation. Such systems are known to create measure solutions for the initial value problem. Adding a stronger transversality assumption on the fields, we are able to obtain solutions in $L^\infty$ under optimal fractional $BV$ regularity of the initial data.Our results show that the critical fractional regularity is $s=1/3$. We also construct an initial data that is not in $BV^{1/3}$ but for which a blow-up in $L^\infty $ occurs, proving the optimality of our results.
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Dates et versions

hal-02895603 , version 1 (09-07-2020)
hal-02895603 , version 2 (27-05-2021)
hal-02895603 , version 3 (21-09-2021)

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Citer

Christian Bourdarias, Anupam Pal Choudhury, Billel Guelmame, Stéphane Junca. Entropy solutions in $BV^s$ for a class of triangular systems involving a transport equation. SIAM Journal on Mathematical Analysis, 2022, 54 (1), pp.791-817. ⟨10.1137/20M1351783⟩. ⟨hal-02895603v3⟩
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