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
Article (author)
File in questo prodotto:
File Dimensione Formato  
Mario_Misha_final10.pdf

accesso aperto

Tipologia: Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione 369.5 kB
Formato Adobe PDF
369.5 kB Adobe PDF Visualizza/Apri
FlaMauNek2014.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 2.74 MB
Formato Adobe PDF
2.74 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/642565
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 16
social impact