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

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)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 Holder-type inequality in PM(a,b), as well as establishing estimates of the semigroup generated by the fractional power of Laplacian (-Delta)(gamma) on these spaces. (C) 2011 Elsevier Ltd. All rights reserved.741656185630Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq