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Analyticity and Gevrey-Class Regularity for the Second-Grade Fluid Equations

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Abstract

We address the global persistence of analyticity and Gevrey-class regularity of solutions to the two and three-dimensional visco-elastic second-grade fluid equations. We obtain an explicit novel lower bound on the radius of analyticity of the solutions that does not vanish as t → ∞, and which is independent of the Rivlin–Ericksen material parameter α. Applications to the damped incompressible Euler equations are also given.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université Paris-Sud, 91405, Orsay Cedex, France

    Marius Paicu

  2. Department of Mathematics, The University of Chicago, Chicago, IL, 60637, USA

    Vlad Vicol

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  1. Marius Paicu
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  2. Vlad Vicol
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Correspondence to Marius Paicu.

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Communicated by S. Friedlander

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Paicu, M., Vicol, V. Analyticity and Gevrey-Class Regularity for the Second-Grade Fluid Equations. J. Math. Fluid Mech. 13, 533–555 (2011). https://doi.org/10.1007/s00021-010-0032-z

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