相关论文: Some properties of a non-hydrostatic stochastic oc…
Consider the $3$-d primitive equations in a layer domain $\Omega=G \times (-h,0)$, $G=(0,1)^2$, subject to mixed Dirichlet and Neumann boundary conditions at $z=-h$ and $z=0$, respectively, and the periodic lateral boundary condition. It is…
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. From deterministic viewpoint the 3D Primitive Equations are…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
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…
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 that that the stochastic 3D primitive equations with either the physical boundary conditions or Neumann boundary conditions on the top and bottom and Dirichlet boundary condition on the sides driven by multiplicative…
The dichotomy between noise-stable and (completely) noise-sensitive stochastic models is of recent interest in probability theory. Of particular interest is the study of lattice models coming from statistical physics. The Fourier transform…
We establish the conditioned stochastic stability of equilibrium states for H\"older potentials on uniformly hyperbolic sets. While standard stochastic stability characterises measures on attractors, we analyse the statistics of transient…
In this paper we investigate the stochastic 3D Navier-Stokes equations perturbed by linear multiplicative Gaussian noise of convolution type by transformation to random PDEs. We are not interested in the regularity of the initial data. We…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
This paper presents a joint theoretical and numerical study of a stochastic version of the compressible Navier-Stokes equations within the location uncertainty (LU) framework, applied to problems related to upper ocean vertical mixing. This…
In the classical work [FK], Fujita and Kato established the local existence of solutions to the 3D Navier-Stokes equations in the critical $\mathbb{H}^{1/2}$-space. In this paper, we are concerned with the global well-posedness of the…
The 3D primitive equations are used in most geophysical fluid models to approximate the large scale oceanic and atmospheric dynamics. We prove that there do not exist smooth stationary solutions to the 3D primitive equations with compact…
An important feature of the planetary oceanic dynamics is that the aspect ratio (the ratio of the depth to horizontal width) is very small. As a result, the hydrostatic approximation (balance), derived by performing the formal small aspect…
The work analyzes the stability of the quantum eigenstates when they are submitted to fluctuations by using the stochastic generalization of the Madelung quantum hydrodynamic approach. In the limit of sufficiently slow kinetics, the quantum…
The primitive equations are derived from the $3D$-Navier-Stokes equations by the hydrostatic approximation. Formally, assuming an $\varepsilon$-thin domain and anisotropic viscosities with vertical viscosity…
We study quench dynamics and equilibration in one-dimensional quantum hydrodynamics, which provides effective descriptions of the density and velocity fields in gapless quantum gases. We show that the information content of the large time…
In this paper, we consider the initial-boundary value problem of the three-dimensional primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and horizontal diffusivity. We establish the local, in time,…
In this paper, we present a numerical analysis of the hydrostatic Stokes equations, which are linearization of the primitive equations describing the geophysical flows of the ocean and the atmosphere. The hydrostatic Stokes equations can be…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…