Solution Properties of a 3d Stochastic Euler Fluid Equation
نویسندگان
چکیده
We prove local well posedness in regular spaces and a Beale-Kato-Majda blow-up criterion for a recently derived stochastic model of the 3D Euler fluid equation for incompressible flow. This model describes incompressible fluid motions whose Lagrangian particle paths follow a stochastic process with cylindrical noise and also satisfy Newton’s 2nd Law in every Lagrangian domain.
منابع مشابه
Numerical Solution of Weakly Singular Ito-Volterra Integral Equations via Operational Matrix Method based on Euler Polynomials
Introduction Many problems which appear in different sciences such as physics, engineering, biology, applied mathematics and different branches can be modeled by using deterministic integral equations. Weakly singular integral equation is one of the principle type of integral equations which was introduced by Abel for the first time. These problems are often dependent on a noise source which a...
متن کاملThe Effects of Different SDE Calculus on Dynamics of Nano-Aerosols Motion in Two Phase Flow Systems
Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...
متن کاملNumerical solution of second-order stochastic differential equations with Gaussian random parameters
In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...
متن کاملDeveloping a 3D stochastic discrete fracture network model for hydraulic analyses
Fluid flow in jointed rock mass with impermeable matrix is often controlled by joint properties, including aperture, orientation, spacing, persistence and etc. On the other hand, since the rock mass is made of heterogeneous and anisotropic natural materials, geometric properties of joints may have dispersed values. One of the most powerful methods for simulation of stochastic nature of geometri...
متن کاملStochastic Navier-Stokes Equations for Turbulent Flows
This paper concerns the fluid dynamics modelled by the stochastic flow η̇ (t, x) = u (t,η (t, x)) + σ (t,η (t, x)) ◦ Ẇ η(0, x) = x where the turbulent term is driven by the white noise Ẇ . The motivation for this setting is to understand the motion of fluid parcels in turbulent and randomly forced fluid flows. Stochastic Euler equations for the undetermined components u(t, x) and σ(t, x) o...
متن کامل