On the existence of pullback attractor for a two-dimensional shear flow with Tresca's boundary condition

Tom 81 / 2008

Mahdi Boukrouche, Grzegorz /Lukaszewicz Banach Center Publications 81 (2008), 81-93 MSC: 76D05, 76F10, 76F20. DOI: 10.4064/bc81-0-5

Streszczenie

We consider a two-dimensional Navier-Stokes shear flow with time dependent boundary driving and subject to Tresca law. We establish the existence of a unique global in time solution and then, using a recent method based on the concept of the Kuratowski measure of noncompactness of a bounded set, we prove the existence of the pullback attractor for the associated cocycle. This research is motivated by a problem from lubrication theory.

Autorzy

  • Mahdi BoukroucheLaboratory of Mathematics
    University of Saint-Etienne
    LaMUSE EA-3989
    23 rue du Dr Paul Michelon
    Saint-Etienne, 42023, France
    e-mail
  • Grzegorz /LukaszewiczMathematics Department
    University of Warsaw
    Banacha 2
    02-957 Warszawa, Poland
    e-mail

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