On stochastic modified 3D Navier–Stokes equations with anisotropic viscosity Article

Bessaih, H, Millet, A. (2018). On stochastic modified 3D Navier–Stokes equations with anisotropic viscosity . JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 462(1), 915-956. 10.1016/j.jmaa.2017.12.053

cited authors

  • Bessaih, H; Millet, A

authors

abstract

  • Navier–Stokes equations in the whole space R3 subject to an anisotropic viscosity and a random perturbation of multiplicative type is described. By adding a term of Brinkman–Forchheimer type to the model, existence and uniqueness of global weak solutions in the PDE sense are proved. These are strong solutions in the probability sense. The Brinkman–Forchheirmer term provides some extra regularity in the space L2α+2(R3), with α>1. As a consequence, the nonlinear term has better properties which allow to prove uniqueness. The proof of existence is performed through a control method. A Large Deviations Principle is given and proven at the end of the paper.

publication date

  • June 1, 2018

Digital Object Identifier (DOI)

start page

  • 915

end page

  • 956

volume

  • 462

issue

  • 1