Related papers: Transportation inequalities for stochastic wave eq…
We discuss transport equations resulting from relativistic diffusions in the proper time. We show that a solution of the transport equation can be obtained from the solution of the diffusion equation by means of an integration over the…
Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain non-deterministic in…
We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian…
We consider the stochastic damped nonlinear wave equation $\partial_t^{2}u+\partial_t u+u-\Delta u +u^{3} = \sqrt{2} {\langle{\nabla}\rangle^{-s}} \xi$ on the two-dimensional torus $\mathbb T^2$, where $\xi$ denotes a space-time white noise…
We present a first numerical investigation of the accuracy of the recently proposed {\em non-classical transport equation}. This equation contains an extra independent variable (the path-length $s$), and models particle transport taking…
We describe and analyze the mean transport due to transient progressive waves, including breaking waves. The waves are packets and are generated with a boundary-forced air-water two-phase Navier Stokes solver. The analysis is done in the…
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we…
We study stochastic SQG equations on the torus $\mathbb{T}^2$ with multiplicative transport noise in the $L^2$-setting. Under a suitable scaling of the noise, we show that the solutions converge weakly to the unique solution to the…
In this paper, we study a class of nonlinear space-time fractional stochastic kinetic equations in $\mathbb{R}^d$ with Gaussian noise which is white in time and homogeneous in space. This type of equation constitutes an extension of the…
For a given Lagrangian $L:[0,T]\times M\times M^\ast\rightarrow \mathbb{R}_+$ and probability measures $\mu\in\mathcal{P}(M^\ast)$, $\nu\in \mathcal{P}(M)$, we introduce the stochastic ballistic transportation problems…
We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We present a physical example, where a fractional (both in space and time) Schr\"odinger equation appears only as a formal effective description of diffusive wave transport in complex inhomogeneous media. This description is a result of the…
We consider the optimal transport problem between zero mean Gaussian stationary random fields both in the aperiodic and periodic case. We show that the solution corresponds to a weighted Hellinger distance between the multivariate and…
We prove existence of infinitely many stationary solutions as well as ergodic stationary solutions for the stochastic Navier-Stokes equations on $\mathbb{T}^2$ \begin{align*} \dif u+\div(u\otimes u)\dif t+\nabla p\dif t&=\Delta u\dif t +…
We consider the stochastic transport equation with a possibly unbounded H\"older continuous vector field. Well-posedness is proved, namely, we show existence, uniqueness and strong stability of W^{1,p}-weak solutions.
In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic…
Let X be the solution of the multidimensional stochastic differential equationdX(t) = b(t, X(t)) dt + sigma(t, X(t)) dW(t)\, with X(0)=x where W is a standard Brownian motion. We show that when b is measurable and sigma is in an appropriate…
In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed.
We study uncertainty in the dynamics of time-dependent flows by identifying barriers and enhancers to stochastic transport. This topological segmentation is closely related to the theory of Lagrangian coherent structures and is based on a…