Article
Long time dynamics for functional three-dimensional Navier-Stokes-Voigt equations
Author/s | Caraballo Garrido, Tomás
Márquez Durán, Antonio Miguel |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2020-06-24 |
Deposit Date | 2021-02-01 |
Published in |
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Abstract | In this paper we consider a non-autonomous Navier-Stokes-Voigt model including a variety of delay terms in a unified formulation. Firstly, we prove the existence and uniqueness of solutions by using a Galerkin scheme. Next, ... In this paper we consider a non-autonomous Navier-Stokes-Voigt model including a variety of delay terms in a unified formulation. Firstly, we prove the existence and uniqueness of solutions by using a Galerkin scheme. Next, we prove the existence and eventual uniqueness of stationary solutions, as well as their exponential stability by using three methods: first, a Lyapunov function which requires differentiability for the delays; next we exploit the Razumikhin technique to weaken the differentiability assumption to just continuity; finally, we use a Gronwall-like type of argument to provide sufficient conditions for the exponential stability in a general case which, in particular, for a situation of variable delay, it only requires measurability of the variable delay function. |
Citation | Caraballo Garrido, T. y Márquez Durán, A.M. (2020). Long time dynamics for functional three-dimensional Navier-Stokes-Voigt equations. AIMS Mathematics, 5 (6), 5470-1-5494-23. |
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