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

Bhattacharya, Rabi; Chen, Larry; Dobson, Scott; Guenther, Ronald; Orum, Chris; Ossiander, Mina; Thomann, Enrique; Waymire, Edward

doi:10.1090/S0002-9947-03-03246-X

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

Trans. Amer. Math. Soc. 355 (2003), 5003-5040 Request permission

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.

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