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Zbl 1156.76019
Iyer, Gautam
A stochastic Lagrangian proof of global existence of the Navier-Stokes equations for flows with small Reynolds number. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 1, 181-189 (2009). ISSN 0294-1449

Summary: We consider the incompressible Navier-Stokes equations with spatially periodic boundary conditions. If the Reynolds number is small enough, we provide an elementary short proof of the existence of global in time Hölder continuous solutions. Our proof uses a stochastic representation formula to obtain a decay estimate for heat flows in Hölder spaces, and a stochastic Lagrangian formulation of the Navier-Stokes equations.

MSC 2000:: *76D06 Statistical solutions of Navier-Stokes and related equations
76D03 Existence, uniqueness, and regularity theory
35Q30 Stokes and Navier-Stokes equations
60H15 Stochastic partial differential equations

Keywords: decay estimate; Hölder spaces

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