Related papers: The primitive equations with stochastic wind drive…
The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulation Models. For this reason and due to their challenging…
The survival probability and the first-passage-time statistics are important quantities in different fields. The Wiener process is the simplest stochastic processwith continuous variables, and important results can be explicitly found from…
In this paper, we investigate how weakening the classical hydrostatic balance hypothesis impacts the well-posedness of the stochastic LU primitive equations. The models we consider are intermediate between the incompressible 3D LU…
Due to the absence of dynamical equation in the vertical momentum component of the primitive equations (PEs) of atmospheric dynamics, the vertical component of the velocity can be recovered only from the information on the other physical…
The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions…
We consider stochastic differential equations driven by Wiener processes. The vector fields are supposed to satisfy only local Lipschitz conditions. The Lipschitz constants of the drift vector field, valid on balls of radius $R$, are…
Stochastic versions of a classical model for natural ventilation are proposed and investigated to demonstrate the effect of random fluctuations on stability and predictability. In a stochastic context, the well-known deterministic result…
The inviscid multi-layer quasi-geostrophic equations are considered over an arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions are imposed to accommodate the free fluctuations of the top and layer interfaces.…
We introduce new boundary conditions for differential forms on symplectic manifolds with boundary. These boundary conditions, dependent on the symplectic structure, allows us to write down elliptic boundary value problems for both…
Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary interaction. To solve the equation we transform…
A finite element method for the numerical solution of the anisotropic Navier-Stokes equations in shallow domain is presented. This method take into account aspect ratio in the hydrostatic approximation of the Navier-Stokes equations…
We study the barotropic compressible Navier-Stokes equations with Navier-type boundary condition in a two-dimensional simply connected bounded domain with $C^{\infty}$ boundary $\partial\Omega.$ By some new estimates on the boundary related…
We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero…
A modification of the classical primitive equations of the atmosphere is considered in order to take into account important phase transition phenomena due to air saturation and condensation. We provide a mathematical formulation of the…
In this contribution we develop a solution theory for singular quasilinear stochastic partial differential equations subject to an initial condition. We obtain our solution theory as a perturbation of the rough path approach developed to…
The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…
We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mild solution is positive if the initial datum is positive. As…
This paper presents a spatially and temporally adaptive boundary condition to specify the volumetric flux for lattice Boltzmann methods. The approach differs from standard velocity boundary conditions because it allows the velocity to vary…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
We study a mathematical model of a compressible viscous fluid driven by stochastic forces under slip boundary conditions of friction type. We introduce a notion of a weak solution that is analytically and probabilistically consistent with…