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Global Existence of Solutions to 2-D Navier–Stokes Flow with Non-decaying Initial Data in Exterior Domains

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Abstract

We study the two dimensional Navier–Stokes initial boundary value problem in exterior domains assuming that the initial data \(u_0\) belongs \(L^\infty \). The global (in time) unique existence of this problem is furnished. The behavior of \(||u(t)||_\infty \) for large t is of double exponential kind.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università degli Studi della Campania, “L. Vanvitelli” via Vivaldi 43, 81100, Caserta, Italy

    Paolo Maremonti

  2. Graduate School of Human and Environmental Studies, Kyoto University, Yoshida-nihonmatsu-cho, Sakyo-ku, Kyoto, 606-8501, Japan

    Senjo Shimizu

Authors
  1. Paolo Maremonti
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  2. Senjo Shimizu
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Correspondence to Paolo Maremonti.

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Communicated by Y. Giga

The research of P.M. was partially supported by GNFM (INdAM) and by MIUR via the PRIN 2012 “Nonlinear Hyperbolic Partial Differential Equations, Dispersive and Transport Equations: Theoretical and Applicative Aspects”. The research of S.S. was partially supported by JSPS Grant-in-Aid for Scientific Research (B)—16H03945, MEXT. The latter grant supported a visit of P.M. in Kyoto University.

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Maremonti, P., Shimizu, S. Global Existence of Solutions to 2-D Navier–Stokes Flow with Non-decaying Initial Data in Exterior Domains. J. Math. Fluid Mech. 20, 899–927 (2018). https://doi.org/10.1007/s00021-017-0348-z

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  • DOI: https://doi.org/10.1007/s00021-017-0348-z

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