Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations

Rabindra N Bhattacharya, Larry Chen, Scott Dobson, Ronald B. Guenther, Chris Orum, Mina Ossiander, Enrique Thomann, Edward C. Waymire

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

A general method is developed to obtain conditions on initial data and forcing terms for the global existence of unique regular solutions to incompressible 3d Navier-Stokes equations. The basic idea generalizes a probabilistic approach introduced by LeJan and Sznitman (1997) to obtain weak solutions whose Fourier transform may be represented by an expected value of a stochastic cascade. A functional analytic framework is also developed which partially connects stochastic iterations and certain Picard iterates. Some local existence and uniqueness results are also obtained by contractive mapping conditions on the Picard iteration.

Original languageEnglish (US)
Pages (from-to)5003-5040
Number of pages38
JournalTransactions of the American Mathematical Society
Volume355
Issue number12
DOIs
StatePublished - Dec 2003

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Incompressible Navier-Stokes Equations
Navier Stokes equations
Cascade
Fourier transforms
kernel
Picard Iteration
Contractive Mapping
Regular Solution
Forcing Term
Local Existence
Existence and Uniqueness Results
Probabilistic Approach
Expected Value
Iterate
Global Existence
Weak Solution
Fourier transform
Navier-Stokes Equations
Iteration
Generalise

Keywords

  • Branching random walk
  • Feynman-Kac
  • Incompressible Navier-Stokes
  • Multiplicative cascade
  • Reaction-diffusion

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations. / Bhattacharya, Rabindra N; Chen, Larry; Dobson, Scott; Guenther, Ronald B.; Orum, Chris; Ossiander, Mina; Thomann, Enrique; Waymire, Edward C.

In: Transactions of the American Mathematical Society, Vol. 355, No. 12, 12.2003, p. 5003-5040.

Research output: Contribution to journalArticle

Bhattacharya, Rabindra N ; Chen, Larry ; Dobson, Scott ; Guenther, Ronald B. ; Orum, Chris ; Ossiander, Mina ; Thomann, Enrique ; Waymire, Edward C. / Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations. In: Transactions of the American Mathematical Society. 2003 ; Vol. 355, No. 12. pp. 5003-5040.
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