On the blow up of a non-local transport equation in compact manifolds

On the blow up of a non-local transport equation in compact manifolds

In this note we show finite time blow-up for a class of non-local active scalar equations on compact Riemannian manifolds. The strategy we follow was introduced by Silvestre and Vicol [Trans. Amer. Math. Soc. 368 (2016), pp. 6159–6188] to deal with the one dimensional Córdoba-Córdoba-Fontelos equati...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2023-02, Vol.151 (2), p.723-735
Hauptverfasser: Alonso-Orán, Diego, Martínez, Ángel David
Format: Artikel
Sprache:eng
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Research article
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Zusammenfassung:In this note we show finite time blow-up for a class of non-local active scalar equations on compact Riemannian manifolds. The strategy we follow was introduced by Silvestre and Vicol [Trans. Amer. Math. Soc. 368 (2016), pp. 6159–6188] to deal with the one dimensional Córdoba-Córdoba-Fontelos equation and might be regarded as an instance of De Giorgi’s method.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/16138