On the regularity of the axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions
Early Career Math Colloquium
On the regularity of the axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions
Series: Early Career Math Colloquium
Seminar
Location: Online
Presenter: Evan Miller, University of British Columbia
In this talk, we will discuss the axisymmetric, swirl-free Euler
equation in four and higher dimensions. We will show that in four and
higher dimensions the axisymmetric, swirl-free Euler equation has
properties which could allow finite-time singularity formation of a form
that is excluded in three dimensions. We will also consider a model
equation that is obtained by taking the infinite-dimensional limit of the
vorticity equation in this setup. This model exhibits finite-time blowup of
a Burgers shock type. The blowup result for the infinite dimensional model
equation heavily suggests that smooth solutions of the Euler equation
exhibit finite-time blowup in sufficiently high dimensions.