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
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author Colombo, Maria
Haffter, Silja
author_facet Colombo, Maria
Haffter, Silja
author_sort Colombo, Maria
collection PubMed
description 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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spelling pubmed-85506172021-11-10 Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation Colombo, Maria Haffter, Silja Ann PDE Manuscript 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] . Springer International Publishing 2021-03-26 2021 /pmc/articles/PMC8550617/ /pubmed/34778719 http://dx.doi.org/10.1007/s40818-021-00093-3 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Manuscript
Colombo, Maria
Haffter, Silja
Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation
title Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation
title_full Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation
title_fullStr Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation
title_full_unstemmed Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation
title_short Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation
title_sort estimate on the dimension of the singular set of the supercritical surface quasigeostrophic equation
topic Manuscript
url 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
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