Remarks on the Blowup Criteria for Oldroyd Models

2009/07/16 by Zhen Lei, Nader Masmoudi, Lei, Zhen +3 · 1 citation
Computer Science · Engineering · Mathematics · #76D03 #76D09 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:76D03 #msc:76D09

paper · pdf · doi:10.48550/arxiv.0907.2745

to appear in JDE

arxiv created 2009/07/16 · openalex publication_date 2009/07/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a new method to prove and improve the Chemin-Masmoudi criterion for viscoelastic systems of Oldroyd type in \citeCM in two space dimensions. Our method is much easier than the one based on the well-known losing a priori estimate and is expected to be easily adopted to other problems involving the losing a priori estimate.

Citations

• Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type
• BKM's Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity
• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations

Cited by

• Uniform vanishing damping limit for the 2D inviscid Oldroyd-B model with fractional stress tensor diffusion
• Large global solutions to the Oldroyd-B model with dissipation

Related

• Global Regularity for some Oldroyd-B type Models
• On the initial-boundary value problem for the 2D partially dissipative Oldroyd-B model: global well-posedness and large time stability
• Global wellposedness to the n-dimensional compressible Oldroyd-B model without damping mechanism
• Backward Euler method for the Equations of Motion Arising in Oldroyd Fluids of Order One with Nonsmooth Initial Data
• Backward Euler method for the equations of motion arising in Oldroyd model of order one with nonsmooth initial data