[图书][B] Stochastic equations in infinite dimensions
G Da Prato, J Zabczyk - 2014 - books.google.com
Now in its second edition, this book gives a systematic and self-contained presentation of
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …
[HTML][HTML] High mode transport noise improves vorticity blow-up control in 3D Navier–Stokes equations
F Flandoli, D Luo - Probability Theory and Related Fields, 2021 - Springer
The paper is concerned with the problem of regularization by noise of 3D Navier–Stokes
equations. As opposed to several attempts made with additive noise which remained …
equations. As opposed to several attempts made with additive noise which remained …
[图书][B] Random Perturbation of PDEs and Fluid Dynamic Models: École d'été de Probabilités de Saint-Flour XL–2010
F Flandoli - 2011 - books.google.com
This volume deals with the random perturbation of PDEs which lack well-posedness, mainly
because of their non-uniqueness, in some cases because of blow-up. The aim is to show …
because of their non-uniqueness, in some cases because of blow-up. The aim is to show …
Ergodicity of stochastic differential equations with jumps and singular coefficients
L Xie, X Zhang - 2020 - projecteuclid.org
We show the strong well-posedness of SDEs driven by general multiplicative Lévy noises
with Sobolev diffusion and jump coefficients and integrable drifts. Moreover, we also study …
with Sobolev diffusion and jump coefficients and integrable drifts. Moreover, we also study …
[HTML][HTML] Averaging along irregular curves and regularisation of ODEs
R Catellier, M Gubinelli - Stochastic Processes and their Applications, 2016 - Elsevier
We consider the ordinary differential equation (ODE) dxt= b (t, xt) d t+ dwt where w is a
continuous driving function and b is a time-dependent vector field which possibly is only a …
continuous driving function and b is a time-dependent vector field which possibly is only a …
Second order perturbation theory of two-scale systems in fluid dynamics
A Debussche, U Pappalettera - Journal of the European Mathematical …, 2024 - ems.press
In the present paper we study fast-slow systems of coupled equations from fluid dynamics,
where the fast component is perturbed by additive noise. We prove that, under a suitable …
where the fast component is perturbed by additive noise. We prove that, under a suitable …
Solution properties of a 3D stochastic Euler fluid equation
We prove local well-posedness in regular spaces and a Beale–Kato–Majda blow-up
criterion for a recently derived stochastic model of the 3D Euler fluid equation for …
criterion for a recently derived stochastic model of the 3D Euler fluid equation for …
[HTML][HTML] Lq (Lp)-theory of stochastic differential equations
In this paper we show the weak differentiability of the unique strong solution with respect to
the starting point x as well as Bismut–Elworthy–Li's derivative formula for the following …
the starting point x as well as Bismut–Elworthy–Li's derivative formula for the following …
Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness
L Beck, F Flandoli, M Gubinelli, M Maurelli - 2019 - projecteuclid.org
In this paper linear stochastic transport and continuity equations with drift in critical L^p
spaces are considered. In this situation noise prevents shocks for the transport equation and …
spaces are considered. In this situation noise prevents shocks for the transport equation and …
From additive to transport noise in 2d fluid dynamics
F Flandoli, U Pappalettera - Stochastics and Partial Differential Equations …, 2022 - Springer
Abstract Additive noise in Partial Differential equations, in particular those of fluid
mechanics, has relatively natural motivations. The aim of this work is showing that suitable …
mechanics, has relatively natural motivations. The aim of this work is showing that suitable …