We prove strong uniqueness for a parabolic SPDE involving both the solution v(t, x) and its derivative ∂xv(t, x). The familiar YamadaWatanabe method for proving strong uniqueness might encounter some difficulties here. In fact, the Yamada-Watanabe method is essentially one dimensional, and in our case there are two unknown functions, v and ∂xv. However, Pardoux and Peng’s method of backward dou...

In this paper, we study various dissipative mechanics associated with the Boussinesq systems which model two-dimensional small amplitude long wavelength water waves. We will show that the decay rate for the damped one-directional model equations, such as the KdV and BBM equations, holds for some of the damped Boussinesq systems.

Standard perturbation methods are applied to Euler’s equations of motion governing the capillary-gravity shallow water waves to derive a general higher-order Boussinesq equation involving the small-amplitude parameter, α = a/h0, and long-wavelength parameter, β = (h0/l), where a and l are the actual amplitude and wavelength of the surface wave, and h0 is the height of the undisturbed water surf...

This paper presents a new algorithm based on Model Reference Adaptive System (MRAS) and its stability analysis for sensorless control of Doubly-Fed Induction Generators (DFIGs). The reference and adjustable models of the suggested observer are based on the active power of the machine. A hysteresis block is used in the structure of the adaptation mechanism, and the stability analysis is performe...

We consider the numerical simulation of a three-dimensional two-phase incompressible flow with a viscous interface. The simulation is based on a sharp interface Navier-Stokes model and the Boussinesq-Scriven constitutive law for the interface viscous stress tensor. In the recent paper [Soft Matter 7, 7797–7804, 2011] a model problem with a spherical droplet in a Stokes Poiseuille flow with a Bo...

Abstract. We consider the convection problem of a fluid with viscosity depending on temperature in either a bounded or an exterior domain Ω⊂R ,N =2,3. It is assumed that the temperature is transported without thermal conductance (dissipation) by the velocity field which is described by the Navier-Stokes flow. This model is commonly called the Boussinesq system with partial viscosity. In this pa...