Mild solutions to the time fractional Navier-Stokes equations in R-N

Author(s)

de Carvalho-Neto, Paulo Mendes ^[1] ; Planas, Gabriela ^[1]

Affiliation

^[1] Univ Estadual Campinas, Dept Matemat, Inst Matemat Estat & Comp Cient, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Differential Equations; v. 259, n. 7, p. 2948-2980, OCT 5 2015.
• Web of Science Citations: 32

Abstract

This paper addresses the existence and uniqueness of mild solutions to the Navier-Stokes equations with time fractional differential operator of order alpha is an element of (0, 1). Several interesting properties about the solution are also highlighted, like regularity and decay rate in Lebesgue spaces, which will depend on the fractional exponent alpha. Moreover, it is shown that the L-P-exponent range, which the solution belongs to, is different from the range for the solution of the classical problem with alpha = 1. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 13/00594-8 - A study of fluid dynamics and its relationship with fractional in time derivatives
• Grantee: Paulo Mendes de Carvalho Neto
• Support Opportunities: Scholarships in Brazil - Post-Doctoral