Dynamics of Partial Differential Equations

Volume 11 (2014)

Number 4

Stability of stationary solutions to 2D-Navier-Stokes models with delays

Pages: 345 – 359

DOI: http://dx.doi.org/10.4310/DPDE.2014.v11.n4.a3

Authors

Tomás Caraballo (Depto. de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Spain)

Xiaoying Han (Department of Mathematics and Statistics, Auburn University, Auburn, Alabama, U.S.A.)

Abstract

In this paper we establish some sufficient conditions for the exponential stability of the stationary solution to a two-dimensional Navier-Stokes model with delay in the forcing term. We are able to cover several situation in a single formulation by using functional formulation for the delay. In particular, our results improve some existing ones in the literature, which were only proved for variable delay.

Keywords

Navier-Stokes equations, stability, variable delay, distributed delay, measurable delay

2010 Mathematics Subject Classification

Primary 35B40, 35R10. Secondary 47H20.

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