On the Navier–Stokes equation perturbed by rough transport noise View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03

AUTHORS

Martina Hofmanová, James-Michael Leahy, Torstein Nilssen

ABSTRACT

We consider the Navier–Stokes system in two and three space dimensions perturbed by transport noise and subject to periodic boundary conditions. The noise arises from perturbing the advecting velocity field by space–time-dependent noise that is smooth in space and rough in time. We study the system within the framework of rough path theory and, in particular, the recently developed theory of unbounded rough drivers. We introduce an intrinsic notion of a weak solution of the Navier–Stokes system, establish suitable a priori estimates and prove existence. In two dimensions, we prove that the solution is unique and stable with respect to the driving noise. More... »

PAGES

203-247

References to SciGraph publications

  • 1995-09. Martingale and stationary solutions for stochastic Navier-Stokes equations in PROBABILITY THEORY AND RELATED FIELDS
  • 2014-02. Rough path stability of (semi-)linear SPDEs in PROBABILITY THEORY AND RELATED FIELDS
  • 2014. A Course on Rough Paths, With an Introduction to Regularity Structures in NONE
  • 2014-11. A theory of regularity structures in INVENTIONES MATHEMATICAE
  • 2006-12. Young Integrals and SPDEs in POTENTIAL ANALYSIS
  • 2010-06. Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations in APPLIED MATHEMATICS & OPTIMIZATION
  • 2012-06. Non-linear rough heat equations in PROBABILITY THEORY AND RELATED FIELDS
  • 1936-12. An inequality of the Hölder type, connected with Stieltjes integration in ACTA MATHEMATICA
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    URI

    http://scigraph.springernature.com/pub.10.1007/s00028-018-0473-z

    DOI

    http://dx.doi.org/10.1007/s00028-018-0473-z

    DIMENSIONS

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