413 citations · 1.5k across the 79 of their papers we have counts for
14 papers · 1 filter
Smoluchowski coagulation equation with velocity dependence
Franco Flandoli, Ruojun Huang, Andrea Papini
In the present article we introduce a variant of Smoluchowski's coagulation equation with both position and velocity variables taking a kinetic viewpoint arising as the scaling lim…
On the infinite dimension limit of invariant measures and solutions of Zeitlin's 2D Euler equations
Franco Flandoli, Umberto Pappalettera, Milo Viviani
In this work we consider a finite dimensional approximation for the 2D Euler equations on the sphere, proposed by V. Zeitlin, and show their convergence towards a solution to Euler…
Ill posedness for the full Euler system driven by multiplicative white noise
Elisabetta Chiodaroli, Eduard Feireisl, Franco Flandoli
We consider the Euler system describing the motion of a compressible fluid driven by a multiplicative white noise. We identify a large class of initial data for which the problem i…
Mean field limit of interacting filaments for 3D Euler equations
Hakima Bessaih, Michele Coghi, Franco Flandoli
The 3D Euler equations, precisely local smooth solutions of class with , are obtained as a mean field limit of finite families of interacting curves, the so called vor…
Well-posedness of the vector advection equations by stochastic perturbation
Franco Flandoli, Christian Olivera
A linear stochastic vector advection equation is considered. The equation may model a passive magnetic field in a random fluid. The driving velocity field is a integrable to a cert…
Mean field limit of interacting filaments and vector valued non linear PDEs
Hakima Bessaih, Michele Coghi, Franco Flandoli
Families of interacting curves are considered, with long range, mean field type, interaction. A family of curves defines a 1-current, concentrated on the curves, analog of the…
Propagation of chaos for interacting particles subject to environmental noise
Michele Coghi, Franco Flandoli
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different pa…
Uniqueness for continuity equations in Hilbert spaces with weakly differentiable drift
Giuseppe Da Prato, Franco Flandoli, Michael Röckner
We prove uniqueness for continuity equations in Hilbert spaces . The corresponding drift is assumed to be in a first order Sobolev space with respect to some Gaussian measur…
Remarks on the stochastic transport equation with Hölder drift
Franco Flandoli, Massimiliano Gubinelli, Enrico Priola
We consider a stochastic linear transport equation with a globally Hölder continuous and bounded vector field. Opposite to what happens in the deterministic case where shocks may a…
Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an Hölder drift component
Sandra Cerrai, Giuseppe Da Prato, Franco Flandoli
We prove pathwise uniqueness for an abstract stochastic reaction-diffusion equation in Banach spaces. The drift contains a bounded Hölder term; in spite of this, due to the space-t…
A dyadic model on a tree
David Barbato, Luigi Amedeo Bianchi, Franco Flandoli +1
We study an infinite system of non-linear differential equations coupled in a tree-like structure. This system was previously introduced in the literature and it is the model from…
Random perturbations of nonlinear parabolic systems
Lisa Beck, Franco Flandoli
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed,…
Well Posedness for Positive Dyadic Model
David Barbato, Franco Flandoli, Francesco Morandin
We consider the solutions of the Cauchy problem for a dyadic model of Euler equations. We prove global existence and uniqueness of Leray-Hopf solutions in a rather large class K th…
Well-posedness of the transport equation by stochastic perturbation
Franco Flandoli, Massimiliano Gubinelli, Enrico Priola
We consider the linear transport equation with a globally Holder continuous and bounded vector field. While this deterministic PDE may not be well-posed, we prove that a multiplica…