Evolution problems of Navier–Stokes type with anisotropic diffusion

  • S. N. Antontsev
  • H. B. de OliveiraEmail author
Original Paper


In this work, we consider the evolutive problem for the incompressible Navier–Stokes equations with a general diffusion which can be fully anisotropic. The existence of weak solutions is proved for the associated initial problem supplemented with no-slip boundary conditions. We prove also the properties of extinction in a finite time, exponential time decay and power time decay. With this respect, we consider the important case of a forces fields with possible different behavior in distinct directions. Perturbations of the asymptotically stable equilibrium are established as well.


Anisotropic diffusion Navier–Stokes Existence  Finite time extinction Exponential time decay Power time decay 

Mathematics Subject Classification

35Q35 76D05 35Q30 76D03 35D30 35B40 


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Copyright information

© Springer-Verlag Italia 2015

Authors and Affiliations

  1. 1.CMAFCIO, Universidade de LisboaLisbonPortugal
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.FCT, Universidade do AlgarveFaroPortugal

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