Random perturbation of PDEs and fluid dynamic models

By Franco Flandoli. 2011

307 citations recorded by the source corpus.

Subfields: Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/023169eb0d863656c77ae773300fa76d62ed3c8b

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Citations in the corpus

On the convergence of stochastic transport equations to a deterministic parabolic one (2019, background): “There is now an extensive literature on the topic of regularization by noise for transport equations, see the review [15] and the references in [5].”
Noise Prevents Singularities in Linear Transport Equations (2012, background): “For nonlinear systems there are negative results, like the fact that noise does not prevent shocks in Burgers equation, see [14], and positive results for special kind of singularities (collapse of measure valued solutions) for the vorticity field of 2D Euler equations, see [16], and for 1D Vlasov-P”
Selection of equilibria in a linear quadratic mean-field game (2018, background): “Examples treated in [2] will serve us as a benchmark throughout this paper, but, in fact, we will mostly follow another approach to these examples due to Delarue and Flandoli [18].”
Noiseless regularisation by noise (2020, methodology): “Indeed, in recent years there has been a lot of activity in understanding the possible role of random perturbations to improve the well-posedness of ordinary (or partial) differential equations (ODE/PDE) (see [19] for a recent review).”
Sobolev differentiable stochastic flows for SDEs with singular coefficients: Applications to the transport equation (2012, background): “For an overview of this topic, the reader may also consult the book [13].”
Regularity of Stochastic Kinetic Equations (2016, background): “Results of this nature have been proved recently for other equations of transport type, see for instance [19], [16], [18], [2], but here, for the first time, we deal with the case of “degenerate” noise, because dWt acts only on a component of the system.”
Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift (2011, methodology): “vel, this work generalizes [5] devoted to the case where B is bounded and in addition H¨older continuous, but with no restriction on the initial conditions. To prove our result we use some ideas from [5, 10, 13, 14] and [23]. The extension of Veretennikov’s result [33] and also of [23] to inﬁnite di”