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SUMMARY:SDEs and linear SPDEs with rough coefficients arising from fluid d
 ynamics 
DTSTART:20120329T101500
DTEND:20120329T111500
DTSTAMP:20260510T053523Z
UID:c97743f43b7da730f3f99a9a8a8e3ea1d13f7deac40b0b9f2f1372e5
CATEGORIES:Conferences - Seminars
DESCRIPTION:Mario Maurelli\nIn this talk I will consider the problem of pa
 thwise uniqueness for stochastic continuity equations (SCEs) and similar e
 quations\, in the case of rough coefficients. The SCE represents the evolu
 tion of a mass driven by the associated SDE and therefore is useful to cap
 ture regularization-by-noise phenomena and splitting/coalescence behaviour
  of the mass. I will state the classical rigorous link between an ODE and 
 the associated continuity equation (superposition principle)\, its general
 ization for an additive noise and the consequences of this link ([1]\, [2]
 ). Then\, I will show Le Jan's theory\, which uses Wiener chaos decomposit
 ion and selects a unique Wiener generalized solution to a SCE ([3]). This 
 is suitable for models arising in fluid dynamics\, in cases of non strong 
 uniqueness\, but can also be applied to restore uniqueness\, starting from
  an ill-posed linear PDE ([4]). Further research directions will be mentio
 ned.
LOCATION:AAC006 http://plan.epfl.ch/?zoom=20&recenter_y=5864224.42038&rece
 nter_x=730672.24955&layerNodes=fonds\,batiments\,labels\,information\,park
 ings_publics\,arrets_metro&floor=0&q=AAC006
STATUS:CONFIRMED
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