On 3D Navier-Stokes equations: regularization and uniqueness by delays

A modified version of the three dimensional Navier-Stokes equations is considered with periodic boundary conditions. A bounded constant delay is introduced into the convective term, that produces a regularizing effect on the solution. In fact, by assuming appropriate regularity on the initial data,...

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Detalles Bibliográficos
Autores: Bessaih, Hakima, Garrido Atienza, María José, Schmalfuss, Björn
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2018
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/75707
Acceso en línea:https://hdl.handle.net/11441/75707
https://doi.org/10.1016/j.physd.2018.03.004
Access Level:acceso abierto
Palabra clave:3D Navier-Stokes equations
Delayed equations
Uniqueness
Global weak solutions
Descripción
Sumario:A modified version of the three dimensional Navier-Stokes equations is considered with periodic boundary conditions. A bounded constant delay is introduced into the convective term, that produces a regularizing effect on the solution. In fact, by assuming appropriate regularity on the initial data, the solutions of the delayed equations are proved to be regular and, as a consequence, existence and also uniqueness of a global weak solution is obtained. Moreover, the associated flow is constructed and the continuity of the semigroup is proved. Finally, we investigate the passage to the limit on the delay, obtaining that the limit is a weak solution of the Navier-Stokes equations.