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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20260305T212318Z
DTSTART:20260318T150000Z
DTEND:20260318T160000Z
SUMMARY:Probability Seminar: Luca Galimberti - WELL-POSEDNESS OF STOCHAST
 IC CONTINUITY EQUATIONS ON RIEMANNIAN MANIFOLDS
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}h1sx-mmdz2s
 nh-vaqsjq
DESCRIPTION:Luca Galimberti (King's College London) will speak at the Pro
 bability seminar.\n\nTitle: WELL-POSEDNESS OF STOCHASTIC CONTINUITY EQUA
 TIONS ON RIEMANNIAN MANIFOLDS\n\nAbstract: We analyze continuity equatio
 ns with Stratonovich stochasticity on a smooth closed and compact Rieman
 nian manifold $M$ with metric $h$. The velocity field $u$ is perturbed b
 y Gaussian noise terms $\\dot W_1(t)\, \\ldots\, \\dot W_N(t)$ driven by
  smooth spatially dependent vector fields $a_1(x)\, \\ldots\, a_N(x)$ on
  $M$. The velocity $u$ belongs to $L^1_t W^{1\,2}_x$ with $\\mathrm{div}
 _h\\\, u$ bounded in $L^p_{t\,x}$ for $p > d+2$\, where $d$ is the dimen
 sion of $M$ (we do not assume $\\mathrm{div}_h\\\, u \\in L^\\infty_{t\,
 x}$). We show that by carefully choosing the noise vector fields $a_i$ (
 and the number $N$ of them)\, the initial-value problem is well-posed in
  the class of weak $L^2$ solutions\, although the problem can be ill-pos
 ed in the deterministic case because of concentration effects. The proof
  of this ``regularization by noise'' result reveals a link between the n
 onlinear structure of the underlying domain $M$ and the noise\, a link t
 hat is somewhat hidden in the Euclidean case (when the $a_i$ are constan
 t). To our knowledge\, this is the first instance of ``regularization by
  noise'' phenomena beyond $\\mathbb{R}^d$. The proof is based on an \\em
 ph{a priori} estimate in $L^2$\, which is obtained by a duality method\,
  and a weak compactness argument.\nThis is a joint work with Kenneth Kar
 lsen (UiO).\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 2\, Alan Turing Building\, Manchester
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