Long time dynamics for functional three-dimensional Navier-Stokes-Voigt equations

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 w...

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Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Márquez Durán, Antonio Miguel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/104386
Acceso en línea:https://hdl.handle.net/11441/104386
https://doi.org/10.3934/math.2020351
Access Level:acceso abierto
Palabra clave:Navier-Stokes-Voigt model
delay
unified formulation
stationary solutions
exponential stability
Razumikhin
Descripción
Sumario: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.