Related papers: Well-posedness Properties for a Stochastic Rotatin…

Generalized Navier-Stokes equations which were proposed recently to describe active turbulence in living fluids are analyzed rigorously. Results on wellposedness and stability in the $L^2(\mathbb{R}^n)$-setting are derived. Due to the…

The initial-value problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system was recently introduced in [4]. It is numerically shown to be stable and a good approximation to the…

In this work, we combine a stochastic model reduction with a particle filter augmented with tempering and jittering, and apply the combined algorithm to a damped and forced incompressible 2D Euler dynamics defined on a simply connected…

In recent years, stochastic parametrizations have been ubiquitous in modelling uncertainty in fluid dynamics models. One source of model uncertainty comes from the coarse graining of the fine-scale data and is in common usage in…

In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and…

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…

We investigate a class of scalar conservation laws on manifolds driven by multiplicative Gaussian (Ito) noise. The Cauchy problem defined on a Riemannian manifold is shown to be well-posed. We prove existence of generalized kinetic…

In this paper we prove well-posedness and stabibility of a class of stochastic delay differential equations with singular drift. Moreover, we show local well-posedness under localized assumptions.

Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent…

We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…

In this paper we introduce a constructive approach to study well-posedness of solutions to stochastic fluid-structure interaction with stochastic noise. We focus on a benchmark problem in stochastic fluid-structure interaction, and prove…

We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends results of the…

We prove the existence and uniqueness of maximal solutions to the 3D SALT (Stochastic Advection by Lie Transport, [Holm arXiv:1410.8311]) Navier-Stokes Equation in velocity and vorticity form, on the torus and the bounded domain…

The flow of nematic liquid crystals can be described by a highly nonlinear stochastic hydrodynamical model, thus is often influenced by random fluctuations, such as uncertainty in specifying initial conditions and boundary conditions. In…

We show existence and pathwise uniqueness of probabilistically strong solutions to a pseudomonotone stochastic evolution problem on a bounded domain $D\subseteq\mathbb{R}^d$, $d\in\mathbb{N}$, with homogeneous Dirichlet boundary conditions…

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…

There is a reasonable possibility that the present-day Atlantic Meridional Overturning Circulation is in a bi-stable regime and hence it is relevant to compute probabilities and pathways of noise-induced transitions between the stable…

This work is a continuation of the authors' work for the stochastic 2D Euler equation driven by transport type noise. Here we lift the incompressibility constraint. Instead we assume a weighted incompressibility condition. This condition is…

We consider stochastic inviscid dyadic models with energy-preserving noise. It is shown that the models admit weak solutions which are unique in law. Under a certain scaling limit of the noise, the stochastic models converge weakly to a…

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension $N\geq2$. We address the question of well-posedness for {\it large} data having critical Besov regularity. Our result improve the analysis of R.…