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Singularity formation for the fractional Euler-alignment system in 1D.
- Source :
- Transactions of the American Mathematical Society; Jan2021, Vol. 374 Issue 1, p487-514, 28p
- Publication Year :
- 2021
-
Abstract
- We study the formation of singularities for the Euler-alignment system with influence function ψ = k<subscript>α</subscript> / |x|<superscript>1+α</superscript> in 1D. As in [Commun. Math. Sci. 17 (2019), pp. 1779-1794] the problem is reduced to the analysis of a nonlocal 1D equation. We show the existence of singularities in finite time for any α in the range 0 < α < 2 in both the real line and the periodic case and with just a point of vacuum. [ABSTRACT FROM AUTHOR]
- Subjects :
- EULER equations
VACUUM
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 374
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 147640980
- Full Text :
- https://doi.org/10.1090/tran/8228