On the local solvability in Morrey spaces of the Navier-Stokes equations in a rotating frame

Author(s)

de Almeida, Marcelo Fernandes ^[1] ; Ferreira, Lucas C. F. ^[1]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Dept Matemat, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 405, n. 2, p. 362-372, SEP 15 2013.
• Web of Science Citations: 1

Abstract

We prove local-in-time (non-uniform) solvability for the rotating Navier-Stokes equations in Morrey spaces M-p,mu(sigma)(R-3). These spaces contain singular and nondecaying functions which are of interest in statistical turbulence. We give an algebraic relation between the size of existence time and angular velocity Omega. The evolution of velocity u is analyzed in suitable Kato-Fujita spaces based on Morrey spaces. We show the asymptotic behavior u(Omega) -> w in L-infinity(0, T; M-p,mu(sigma)(R-3)) as Omega -> 0, where w is the solution for the Navier-Stokes equations with the same data u(0). Particularly, for mu = 3 - p, the solution is approximately self-similar for small vertical bar Omega vertical bar, when u(0) is homogeneous of degree - 1. (c) 2013 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 11/00334-0 - Existence and asymptotic behavior for flows of Navier-Stokes fluids under rotational influences
• Grantee: Marcelo Fernandes de Almeida
• Support Opportunities: Scholarships in Brazil - Post-Doctoral