JournalsaihpcVol. 26, No. 1pp. 181–189

A stochastic Lagrangian proof of global existence of the Navier–Stokes equations for flows with small Reynolds number

  • Gautam Iyer

    Department of Mathematics, Stanford University, USA
A stochastic Lagrangian proof of global existence of the Navier–Stokes equations for flows with small Reynolds number cover
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Abstract

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.

Cite this article

Gautam Iyer, A stochastic Lagrangian proof of global existence of the Navier–Stokes equations for flows with small Reynolds number. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 1, pp. 181–189

DOI 10.1016/J.ANIHPC.2007.10.003