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Détails bibliographiques
Auteurs principaux: Fjordholm, Ulrik Skre, Mæhlen, Ola Isaac Høgåsen
Format: Preprint
Publié: 2025
Sujets:
Accès en ligne:https://arxiv.org/abs/2502.11531
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Table des matières:
  • We consider the transport equation with a velocity field satisfying the Osgood condition. The weak formulation is not meaningful in the usual Lebesgue sense, meaning that the usual DiPerna--Lions treatment of the problem is not applicable {(in particular, the divergence of the velocity might be unbounded)}. Instead, we use Riemann--Stieltjes integration to interpret the weak formulation, leading to a well-posedness theory in regimes not covered by existing works. The most general results are for the one-dimensional problem, with generalisations to multiple dimensions in the particular case of log-Lipschitz velocities.