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Global solutions of aggregation equations and other flows with random diffusion

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Main Authors: Matthew, Rosenzweig, Gigliola, Staffilani
Format: Book
Language:English
Published: Springer 2023
Subjects:
parabolic-elliptic Patlak–Keller–Segel model
SQG equation
Online Access:https://link.springer.com/article/10.1007/s00440-022-01171-8
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7462
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spelling oai:localhost:PNK-74622023-04-04T01:53:05Z Global solutions of aggregation equations and other flows with random diffusion Matthew, Rosenzweig Gigliola, Staffilani parabolic-elliptic Patlak–Keller–Segel model SQG equation CC BY Aggregation equations, such as the parabolic-elliptic Patlak–Keller–Segel model, are known to have an optimal threshold for global existence versus finite-time blow-up. In particular, if the diffusion is absent, then all smooth solutions with finite second moment can exist only locally in time. Nevertheless, one can ask whether global existence can be restored by adding a suitable noise to the equation, so that the dynamics are now stochastic. Inspired by the work of Buckmaster et al. (Int Math Res Not IMRN 23:9370–9385, 2020) showing that, with high probability, the inviscid SQG equation with random diffusion has global classical solutions, we investigate whether suitable random diffusion can restore global existence for a large class of active scalar equations in arbitrary dimension with possibly singular velocity fields. 2023-04-04T01:53:05Z 2023-04-04T01:53:05Z 2022 Book https://link.springer.com/article/10.1007/s00440-022-01171-8 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7462 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic parabolic-elliptic Patlak–Keller–Segel model
SQG equation
spellingShingle parabolic-elliptic Patlak–Keller–Segel model
SQG equation
Matthew, Rosenzweig
Gigliola, Staffilani
Global solutions of aggregation equations and other flows with random diffusion
description CC BY
format Book
author Matthew, Rosenzweig
Gigliola, Staffilani
author_facet Matthew, Rosenzweig
Gigliola, Staffilani
author_sort Matthew, Rosenzweig
title Global solutions of aggregation equations and other flows with random diffusion
title_short Global solutions of aggregation equations and other flows with random diffusion
title_full Global solutions of aggregation equations and other flows with random diffusion
title_fullStr Global solutions of aggregation equations and other flows with random diffusion
title_full_unstemmed Global solutions of aggregation equations and other flows with random diffusion
title_sort global solutions of aggregation equations and other flows with random diffusion
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00440-022-01171-8
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7462
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score 8.893527

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