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On the (x,t) asymptotic properties of solutions of the Navier-Stokes equations in the half-space

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Abstract

We study the space-time asymptotic behavior of classical solutions of the initial-boundary value problem for the Navier-Stokes system in the half-space. We construct a (local in time) solution corresponding to an initial data that is only assumed to be continuous and decreasing at infinity as |x|−µ, µ ∈ (1/2,n). We prove pointwise estimates in the space variable. Moreover, if μ ∈ [1, n) and the initial data is suitably small, then the above solutions are global (in time), and we prove space-time pointwise estimates. Bibliography: 19 titles.

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Authors and Affiliations

  1. Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Italy

    F. Crispo & P. Maremonti

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  1. F. Crispo
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  2. P. Maremonti
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Alla memoria di Olga Aleksandrovna Ladyzhenskaya

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 147–202.

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Crispo, F., Maremonti, P. On the (x,t) asymptotic properties of solutions of the Navier-Stokes equations in the half-space. J Math Sci 136, 3735–3767 (2006). https://doi.org/10.1007/s10958-006-0197-4

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  • DOI: https://doi.org/10.1007/s10958-006-0197-4

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