Abstract
We present a general covariance property and use it to prove that proper nondegenerate self-similar blow-up is not possible for active scalar equations.
Similar content being viewed by others
REFERENCES
P. Constantin, Geometric and analytic studies in turbulences, in Trends and Perspectives in Appl. Math., L. Sirovich, ed., Appl. Math. Sciences, Vol. 100 (Springer-Verlag, 1994).
P. Constantin, A. Majda, and E. Tabak, Formation of strong fronts in the 2D quasigeostrophic thermal active scalar, Nonlinearity 7:1495–1533 (1994).
P. Constantin, Q. Nie, and N. Schoerghofer, work in preparation.
J. T. Beale, T. Kato, and A. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Commun. Math. Phys. 94:61–66 (1984).
P. Constantin, C. Fefferman, and A. Majda, Geometric constraints on potentially singular solutions for the 3-D Euler equations, Commun. in PDE 21:559–571 (1996).
K. Ohkitani and M. Yamada, Hiroshima University preprint.
D. Cordoba, On the geometry of solutions of the quasi-geostrophic active scalar and Euler equations, Proc. Natl. Acad. Sci. USA 94:12769–12770 (1997).
P. Constantin and J. Wu, The inviscid limit for non-smooth vorticity, Indiana Univ. Math. J. 45:67–81 (1996).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Constantin, P. Absence of Proper Nondegenerate Generalized Self-Similar Singularities. Journal of Statistical Physics 93, 777–786 (1998). https://doi.org/10.1023/B:JOSS.0000033162.96173.50
Issue Date:
DOI: https://doi.org/10.1023/B:JOSS.0000033162.96173.50