Nonuniqueness of nematic liquid crystal flows in dimension three

TL;DR

This paper demonstrates the existence of infinitely many weak solutions to three-dimensional nematic liquid crystal flows, highlighting nonuniqueness and complex behaviors such as backward bubbling.

Contribution

It constructs infinitely many weak solutions for 3D nematic liquid crystal flows with bounded energy, revealing nonuniqueness in this setting.

Findings

Existence of infinitely many weak solutions

Solutions exhibit backward bubbling phenomena

Solutions are axisymmetric with bounded energy

Abstract

For suitable initial and boundary data, we construct infinitely many weak solutions to the nematic liquid crystal flows in dimension three. These solutions are in the axisymmetric class with bounded energy and backward bubbling at a large time.