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

DOI10.1090/S0002-9947-03-03246-XzbMath1031.35115OpenAlexW2074172639MaRDI QIDQ4425456

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

Publication date: 10 September 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-03-03246-x

zbMATH Keywords

reaction-diffusionbranching random walkFeynman-Kacincompressible Navier-Stokesmultiplicative cascade

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stochastic analysis applied to problems in fluid mechanics (76M35) Navier-Stokes equations (35Q30) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

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• Theory of Bessel potentials. I
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Mathematical theory of Feynman path integrals
• Unimodality of infinitely divisible distribution functions of class L
• Fractal Burgers equations
• Stochastic cascades and 3-dimensional Navier-Stokes equations
• On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations
• Littlewood-Paley decomposition and Navier-Stokes equations
• On the Navier-Stokes initial value problem. I
• Finite time blow up for a Navier-Stokes like equation
• Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov
• Une remarque sur l'analyticité des solutions milds des équations de Navier–Stokes dans
• Homogeneity criterion for the Navier-Stokes equations in the whole spaces