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Fractional Navier–Stokes equations and a Hölder-type inequality in a sum of singular spaces

✍ Scribed by Lucas C.F. Ferreira; Elder J. Villamizar-Roa

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
285 KB
Volume
74
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper we study the local well-posedness of the fractional Navier-Stokes system with initial data belonging to a sum of two pseudomeasure-type spaces denoted by PM a,b := PM a + PM b . The proof requires showing a Hölder-type inequality in PM a,b , as well as establishing estimates of the semigroup generated by the fractional power of Laplacian (-∆) γ on these spaces.

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We investigate the sharp constants in a Brézis-Gallouët-Wainger type inequality with a double logarithmic term in the Hölder space in a bounded domain in R n . Ibrahim, Majdoub and Masmoudi gave the sharp constant in the two-dimensional case. We make precise estimates to give the sharp constants, an