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Large time behaviour in incompressible Navier-Stokes equations



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Carpio, Ana (1996) Large time behaviour in incompressible Navier-Stokes equations. Zeitschrift fur angewandte Mathematik und Mechanik, 76 (Sup. 2). pp. 495-496. ISSN 0044-2267

Official URL: http://onlinelibrary.wiley.com/journal/10.1002/%28ISSN%291521-4001



We give a development up to the second order of strong solutions u of incompressible Navier-Stokes equations in R(n), n greater than or equal to 2 for several classes of initial data u(0). The first term is the solution h(t) = G(t) * u(0) of the heat equation taking the same initial data. A better aproximation is provided by the divergence free solutions with initial data u(0) of v(t) - Delta(v) = -h(i) partial derivative(i)h - partial derivative(j) del E(n)* h(i) partial derivative(i)h(j) in R(+) x R(n) where E(n) stands for the fundamental solution of -Delta in R(n). For initial data satisfying some integrability conditions(and small enough, if n greater than or equal to 3) we obtain, for 1 less than or equal to q less than or equal to infinity, [GRAPHICS] when t --> infinity, where delta(t) is equal to log t if n = 2 and to a constant if n greater than or equal to 3 and R(t) is a corrector term that we compute explicitely.

Item Type:Article
Subjects:Sciences > Mathematics > Differential equations
ID Code:15185
Deposited On:11 May 2012 08:35
Last Modified:12 Dec 2018 15:08

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