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Finite-time singularity formation for an active scalar equation

Publication ,  Journal Article
Elgindi, T; Ibrahim, S; Shen, S
Published in: Nonlinearity
July 1, 2021

We introduce an active scalar equation with a similar structure to the 3D Euler equations. Through studying the behavior of scale-invariant solutions, we show that compactly supported Lipschitz solutions belonging to CR2 0 can become singular in finite time. The interesting feature here is that we can achieve this in the absence of spatial boundaries.

Duke Scholars

Published In

Nonlinearity

DOI

EISSN

1361-6544

ISSN

0951-7715

Publication Date

July 1, 2021

Volume

34

Issue

7

Start / End Page

5045 / 5069

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Elgindi, T., Ibrahim, S., & Shen, S. (2021). Finite-time singularity formation for an active scalar equation. Nonlinearity, 34(7), 5045–5069. https://doi.org/10.1088/1361-6544/ac0231
Elgindi, T., S. Ibrahim, and S. Shen. “Finite-time singularity formation for an active scalar equation.” Nonlinearity 34, no. 7 (July 1, 2021): 5045–69. https://doi.org/10.1088/1361-6544/ac0231.
Elgindi T, Ibrahim S, Shen S. Finite-time singularity formation for an active scalar equation. Nonlinearity. 2021 Jul 1;34(7):5045–69.
Elgindi, T., et al. “Finite-time singularity formation for an active scalar equation.” Nonlinearity, vol. 34, no. 7, July 2021, pp. 5045–69. Scopus, doi:10.1088/1361-6544/ac0231.
Elgindi T, Ibrahim S, Shen S. Finite-time singularity formation for an active scalar equation. Nonlinearity. 2021 Jul 1;34(7):5045–5069.
Journal cover image

Published In

Nonlinearity

DOI

EISSN

1361-6544

ISSN

0951-7715

Publication Date

July 1, 2021

Volume

34

Issue

7

Start / End Page

5045 / 5069

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics