Vanishing viscosity limit of the 3D incompressible Oldroyd-B model

Zi, Ruizhao

doi:10.1016/j.anihpc.2021.02.003

Zi, Ruizhao ¹

¹ School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, PR China

Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1841-1867.

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Résumé

Consider the vanishing viscosity limit of the 3D incompressible Oldroyd-B model. It is shown that this set of equations admits a unique global solution with small analytic data uniformly in the coupling parameter ω close to 1 that corresponds to the inviscid case. We justify the limit from the Oldroyd-B model to the inviscid case $ω = 1$ for all time. Moreover, if the nonlinear term $g_{α} (τ, \nabla u)$ is ignored, similar results hold without resorting to the analytic regularity.

Reçu le : 2020-06-16
Révisé le : 2021-01-27
Accepté le : 2021-02-03

DOI : 10.1016/j.anihpc.2021.02.003

Classification : 76A10, 76B03
Mots-clés : Oldroyd-B model, Global well-posedness, Inviscid limit

Affiliations des auteurs :

Zi, Ruizhao ¹

¹ School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, PR China

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     title = {Vanishing viscosity limit of the {3D} incompressible {Oldroyd-B} model},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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     publisher = {Elsevier},
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Zi, Ruizhao. Vanishing viscosity limit of the 3D incompressible Oldroyd-B model. Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1841-1867. doi : 10.1016/j.anihpc.2021.02.003. http://www.numdam.org/articles/10.1016/j.anihpc.2021.02.003/

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