DE ANNA, Francesco; PAICU, Marius

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DE ANNA, Francesco
Institut de Mathématiques de Bordeaux [IMB]

PAICU, Marius
Institut de Mathématiques de Bordeaux [IMB]

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Journal of Functional Analysis. 2020

Elsevier

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2020

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In this paper, we investigate the Cauchy problem associated to a system of PDE's of Johnson-Segalman type. The considered model describes the evolution of certain viscoelastic fluids within a corotational framework. We show that some widespread results concerning the incompressible Navier-Stokes equations can be extended to the considered system. In particular we show the existence and uniqueness of finite energy solutions for large data in dimension two. This result is supported by suitable condition on the initial data to provide a global-in-time Lipschitz regularity for the flow, which allows to overcome specific challenging due to the non time decay of the main forcing terms. Secondly, we address the global-in-time well posedness of our model in dimension d ≥ 3 in suitable critical spaces. We always allow a Lipschitz regularity of the flow and the initial data are just assumed to be small in a critical weak Lebesgue norm.< Réduire

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finite energy solutions

Johnson-Segalman model

critical regularities.

Lipschitz flow

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The Fujita-Kato Theorem for some Oldroyd-B Models

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