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Article Dans Une Revue Stochastics and Partial Differential Equations: Analysis and Computations Année : 2016

Rough linear transport equation with an irregular drift

Résumé

We study the linear transport equation \[ \frac{\partial}{\partial t} u ( t,x ) +b ( t,x ) \cdot \nabla u ( t,x ) + \nabla u ( t,x ) \cdot \frac{\partial}{\partial t} X ( t ) =0, \hspace{2em} u ( 0,x ) =u_{0} ( x ) \] where $b$ is a vectorfield of limited regularity and $X$ a vector-valued H\"older continuous driving term. Using the theory of controlled rough paths we give a meaning to the weak formulation of the PDE and solve that equation for smooth vectorfields $b$. In the case of the fractional Brownian motion a phenomenon of regularization by noise is displayed.

Dates et versions

hal-01110491 , version 1 (28-01-2015)

Identifiants

Citer

Rémi Catellier. Rough linear transport equation with an irregular drift. Stochastics and Partial Differential Equations: Analysis and Computations, 2016, 4 (3), pp.477-534. ⟨10.1007/s40072-016-0069-y⟩. ⟨hal-01110491⟩
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