Publications [#357911] of Alexander A. Kiselev

Papers Published

1. Kiselev, AA, Small Scale Creation in Active Scalars, in Lecture Notes in Mathematics, PROGRESS IN MATHEMATICAL FLUID DYNAMICS, vol. 2272 (2020), pp. 123-159, ISBN 978-3-030-54898-8 [doi]
   (last updated on 2025/01/30)

   Abstract:
   The focus of the course is on small scale formation in solutions of the incompressible Euler equation of fluid dynamics and associated models. We first review the regularity results and examples of small scale growth in two dimensions. Then we discuss a specific singular scenario for the three-dimensional Euler equation discovered by Hou and Luo, and analyze some associated models. Finally, we will also talk about the surface quasi-geostrophic (SQG) equation, and construct an example of singularity formation in the modified SQG patch solutions as well as examples of unbounded growth of derivatives for the smooth solutions.