Abstract
We describe the structure of solutions developing singularities in the form of cusps in finite time in nonlocal transport equations of the family: where H represents the Hilbert transform. Equations of this type appear in various contexts: evolution of vortex sheets, models for quasi-geostrophic equation and evolution equations for order parameters. Equation (1) was studied in [1] and [2], and the existence of singularities developing in finite time was proved. The structure of such singularities was, nevertheless, not described. In this paper, we will describe the geometry of the solution in the neighborhood of the singularity once it develops and the (self-similar) way in which it is approached as t → t0, where t0 is the singular time.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
