Singular solutions with vorticity control for a nonlocal system of evolution equations

TL;DR

This paper studies a nonlocal one-dimensional transport system modeling 3D Euler equations, constructing solutions that blow up in finite time while maintaining control over their behavior.

Contribution

It introduces a method to construct blowup solutions with vorticity control in a nonlocal evolution system related to fluid dynamics.

Findings

Successfully constructs blowup solutions with controlled vorticity

Provides insights into singularity formation in nonlocal transport equations

Models hyperbolic flow scenarios of 3D Euler equations

Abstract

We investigate a system of nonlocal transport equations in one spatial dimension. The system can be regarded as a model for the 3D Euler equations in the hyperbolic flow scenario. We construct blowup solutions with control up to the blowup time.