We consider the linear transport equation with a globally Hölder continuous and bounded
vector field, with an integrability condition on the divergence. While uniqueness may fail for …

In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …

In this paper, we study the Wong–Zakai approximations given by a stationary process via the
Wiener shift and their associated long term behavior of the stochastic reaction–diffusion …

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 …

In this paper we study the Wong–Zakai approximations given by a stationary process via the
Wiener shift and their associated long term pathwise behavior for the stochastic partial …

We prove that an averaging principle holds for a general class of stochastic reaction–
diffusion systems, having unbounded multiplicative noise, in any space dimension. We show …

These notes originated from a series of lectures given at Waseda University in April–May
2021, supported by Top Global University Project of Waseda University. The first author …

In this paper, we investigate the asymptotic behavior of the solutions of the two-dimensional
stochastic Navier-Stokes equations via the stationary Wong-Zakai approximations given by …

The limit from an Euler-type system to the 2D Euler equations with Stratonovich transport
noise is investigated. A weak convergence result for the vorticity field and a strong …

Nonlinear stochastic rolling is a primary contributor to ship instability. Random wave
excitation is described in this study as a combination of harmonic excitation and Gaussian …