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Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations |
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| Authors: | Rabi N. Bhattacharya Larry Chen Scott Dobson Ronald B. Guenther Chris Orum Mina Ossiander Enrique Thomann Edward C. Waymire |
| Affiliation: | Department of Mathematics, University of Arizona, Tucson, Arizona 85721 ; Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605 ; Department of Mathematics, Linn-Benton Community College, Albany, Oregon 97321 ; Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605 Chris Orum ; Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605 ; Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605 ; Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605 ; Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605 |
| 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. |
| Keywords: | Multiplicative cascade branching random walk incompressible Navier-Stokes Feynman-Kac reaction-diffusion |
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