Global existence in critical spaces for incompressible viscoelastic fluids

2011/01/31 by Ting Zhang, Zhang, Ting, Daoyuan Fang +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.1101.5862

17 pages

arxiv created 2011/01/31 · openalex publication_date 2011/01/31 · arxiv updated 2011/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate local and global strong solutions for the incompressible viscoelastic system of Oldroyd--B type. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations. More precisely, the initial velocity has the same critical regularity index as for the incompressible Navier--Stokes equations, and one more derivative is needed for the deformation tensor. We point out a smoothing effect on the velocity and a L¹-decay on the difference between the deformation tensor and the identity matrix. Our result implies that the deformation tensor F has the same regularity as the density of the compressible Navier--Stokes equations.

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace

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