On the Stochastic Navier–Stokes Equation Driven by Stationary White Noise View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2013

AUTHORS

Chia Ying Lee , Boris Rozovskii

ABSTRACT

We consider an unbiased approximation of stochastic Navier–Stokes equation driven by spatial white noise. This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier–Stokes equation. The nonlinear term can be characterized as the highest stochastic order approximation of the original nonlinear term u ∇ u. We investigate the analytical properties and long-time behavior of the solution. The perturbed equation is solved in the space of generalized stochastic processes using the Cameron–Martin version of the Wiener chaos expansion and generalized Malliavin calculus. We also study the accuracy of the Galerkin approximation of the solutions of the unbiased stochastic Navier–Stokes equations. More... »

PAGES

219-249

References to SciGraph publications

  • 2012-12. On unbiased stochastic Navier–Stokes equations in PROBABILITY THEORY AND RELATED FIELDS
  • 1995-09. Martingale and stationary solutions for stochastic Navier-Stokes equations in PROBABILITY THEORY AND RELATED FIELDS
  • 1994-12. Dissipativity and invariant measures for stochastic Navier-Stokes equations in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
  • Book

    TITLE

    Malliavin Calculus and Stochastic Analysis

    ISBN

    978-1-4614-5905-7
    978-1-4614-5906-4

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-1-4614-5906-4_10

    DOI

    http://dx.doi.org/10.1007/978-1-4614-5906-4_10

    DIMENSIONS

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