Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

We consider the SQG equation with dissipation given by a fractional Laplacian of order [Formula: see text] . We introduce a notion of suitable weak solution, which exists for every [Formula: see text] initial datum, and we prove that for such solution the singular set is contained in a compact set i...

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Detalles Bibliográficos
Autores principales: Colombo, Maria, Haffter, Silja
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Manuscript
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550617/
https://www.ncbi.nlm.nih.gov/pubmed/34778719
http://dx.doi.org/10.1007/s40818-021-00093-3
Descripción
Sumario:We consider the SQG equation with dissipation given by a fractional Laplacian of order [Formula: see text] . We introduce a notion of suitable weak solution, which exists for every [Formula: see text] initial datum, and we prove that for such solution the singular set is contained in a compact set in spacetime of Hausdorff dimension at most [Formula: see text] .

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