A linear stochastic vector advection equation is considered; the equation may model a passive magnetic field in a random fluid. When the driving velocity field is rough but deterministic, in particular just Holder continuous and bounded, one can construct examples of infinite stretching of the passive field, arising from smooth initial conditions. The purpose of the paper is to prove that infinite stretching is prevented if the driving velocity field contains in addition a white noise component.

Noise Prevents Infinite Stretching of the Passive Field in a Stochastic Vector Advection Equation / F. Flandoli, M. Maurelli, M. Neklyudov. - In: JOURNAL OF MATHEMATICAL FLUID MECHANICS. - ISSN 1422-6928. - 16:4(2014), pp. 805-822. [10.1007/s00021-014-0187-0]

Noise Prevents Infinite Stretching of the Passive Field in a Stochastic Vector Advection Equation

M. Maurelli;
2014

Abstract

A linear stochastic vector advection equation is considered; the equation may model a passive magnetic field in a random fluid. When the driving velocity field is rough but deterministic, in particular just Holder continuous and bounded, one can construct examples of infinite stretching of the passive field, arising from smooth initial conditions. The purpose of the paper is to prove that infinite stretching is prevented if the driving velocity field contains in addition a white noise component.
Stochastic vector advection equations; blow-up; regularization by noise; stochastic flows
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore MAT/05 - Analisi Matematica
2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/642565
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