Sharp Estimates for Turbulence in White-Forced Generalised Burgers Equation

Article Article scientifique Article Sharp Estimates for Turbulence in White-Forced Generalised Burgers Equation eng 2013 author Boritchev Alexandre 811118 1730-1771 10.1007/s00039-013-0245-4 1016-443X Here f is strongly convex and satisfies a growth condition, ν is small and positive, while η is a random forcing term, smooth in space and white in time. For any solution u of this equation we consider the quasi-stationary regime, corresponding to t ≥ T1, where T1 depends only on f and on the distribution of η. We obtain sharp upper and lower bounds for Sobolev norms of u averaged in time and in ensemble. These results yield sharp upper and lower bounds for natural analogues of quantities characterising the hydrodynamical turbulence. All our bounds do not depend on the initial condition or on t for t ≥ T1, and hold uniformly in ν. Estimates similar to some of our results have been obtained by Aurell, Frisch, Lutsko and Vergassola on a physical level of rigour; we use an argument from their article. Dewey 500.2 Open Access - Licence nationale Springer 27 Section de physique 13 false Geometric and Functional Analysis 23 6 beba61f4-c3a8-44f6-8347-6467192574df Article (Published version) Public Boritchev2013_Article_SharpEstimatesForTurbulenceInW.pdf 450555 application/pdf openAccess Faculté des sciences / Section de physique

Title	Published in	Access level	OA Policy	Year	Views	Downloads

Sharp Estimates for Turbulence in White-Forced Generalised Burgers Equation	Geometric and Functional Analysis			2013	426	250

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Boritchev, Alexandre