Weak Solution for 3D-Stochastic Third Grade Fluid Equations

Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations

Solution Properties of a 3d Stochastic Euler Fluid Equation

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.

Homotopy Perturbation Solution for Flow of a Third-grade Fluid in Helical Screw Rheometer

This paper provides a theoretical study of steady flow of an incompressible third grade fluid in helical screw rheometer. The model developed in cylindrical coordinates pertains to second order nonlinear coupled differential equations that are solved using homotopy perturbation method. Expressions for velocity components in θ and z−direction are obtained. The volume flow rates are calculated fo...

Optimal Homotopy Asymptotic Solution for Thin Film Flow of a Third Grade Fluid with Partial Slip

The aim of this communication is to investigate thin film flow of an incompressible third grade fluid on an inclined plane with partial slip. The governing equations of this flow are nonlinear and solved for the velocity field using analytical method, name the optimal homotopy asymptotic method (OHAM). Results obtained by OHAM are compared with exact solution and a close agreement was found. Fi...

On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations

Here u, b describe the flow velocity vector and the magnetic field vector respectively, p is a scalar pressure, ν > 0 is the kinematic viscosity, η > 0 is the magnetic diffusivity, while u0 and b0 are the given initial velocity and initial magnetic field with ∇ · u0 = ∇ · b0 = 0. If ν = η = 0, (1.1) is called the ideal MHD equations. As same as the 3D Navier-Stokes equations, the regularity of ...