Existence and Uniqueness of Stationary Solutions for 3D Navier–Stokes System with Small Random Forcing via Stochastic Cascades View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2006-01

AUTHORS

Yuri Bakhtin

ABSTRACT

We consider the 3D Navier–Stokes system in the Fourier space with regular forcing given by a stationary in time stochastic process satisfying a smallness condition. We explicitly construct a stationary solution of the system and prove a uniqueness theorem for this solution in the class of functions with Fourier transform majorized by a certain function h. Moreover we prove the following “one force—one solution” principle: the unique stationary solution at time t is presented as a functional of the realization of the forcing in the past up to t. Our explicit construction of the solution is based upon the stochastic cascade representation. More... »

PAGES

351-360

References to SciGraph publications

  • 2002-09. A Coupling Approach to Randomly Forced Nonlinear PDE's. II in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2001-11. Ergodicity of the 2D Navier--Stokes Equations¶with Random Forcing in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1995-08. Ergodicity of the 2-D Navier-Stokes equation under random perturbations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1997-11. Stochastic cascades and 3-dimensional Navier–Stokes equations in PROBABILITY THEORY AND RELATED FIELDS
  • 2000-09. Stochastic Dissipative PDE's and Gibbs Measures in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2001-11. Gibbsian Dynamics and Ergodicity¶for the Stochastically Forced Navier–Stokes Equation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Journal

    TITLE

    Journal of Statistical Physics

    ISSUE

    2

    VOLUME

    122

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10955-005-8014-x

    DOI

    http://dx.doi.org/10.1007/s10955-005-8014-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1048268586


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