Communications in Mathematical Sciences

Volume 20 (2022)

Number 1

Existence, regularity and weak-strong uniqueness for three-dimensional Peterlin viscoelastic model

Pages: 201 – 230



Aaron Brunk (Institute of Mathematics, Johannes Gutenberg-University, Mainz, Germany)

Yong Lu (Department of Mathematics, Nanjing University, Nanjing, China)

Mária Lukáčová-Medviďová (Institute of Mathematics, Johannes Gutenberg-University, Mainz, Germany)


In this paper we analyze three-dimensional Peterlin viscoelastic model. By means of a mixed Galerkin and semigroup approach we prove the existence of weak solutions. Further, combining parabolic regularity with the relative energy method, we derive a conditional weak-strong uniqueness result.


complex fluids, relative energy, parabolic regularity, weak-strong uniqueness

2010 Mathematics Subject Classification

35A01, 35A02, 35D30, 35Q30, 35Q35, 74D10, 76D03

Received 3 February 2021

Received revised 14 June 2021

Accepted 14 June 2021

Published 10 December 2021