Existence and Uniqueness Results for Two-Dimensional Stochastic Linearised Boussinesq Equation

Abstract

The water flow in saturated zones of the soil is described by two-dimensional Boussinesq equation. This paper is devoted to investigating the linearised stochastic Boussinesq problem in the presence of randomness in hydraulic conductivity, drainable porosity, recharge, evapotranspiration, initial condition and boundary condition. We use the Sabolev spaces and Galerkin method. Under some suitable assumptions, we prove the existence and uniqueness results, as well as, the continuous dependence on the data for the solution of linearised stochastic Boussinesq problem. Keywords: linearised stochastic Boussinesq equation, Galerkin method, existence and uniqueness results, and continuous dependence on the data.