In this article, we analyze the flow of a fluid through a domain modeled using the equations for generalized non-linear Stokes flow coupled with flow through a porous media, modeled using generalized non-linear Darcy flow equations. A prescribed flow rate is assumed specified along the inflow portion of the non-linear Stokes flow boundary. Existence and uniqueness of a variational solution to t...

A review is given of the geodetic concepts necessary for oceanographers to make use of satellite gravity data to define the geoid, and to interpret the resulting product. The geoid is defined, with particular attention to subtleties related to the representation of the permanent tide, and the way in which the geoid is represented in ocean models. 5 The usual spherical harmonic description of th...

The origin of the Earth's lowest geoid, Indian Ocean geoid low (IOGL) has been controversial. predicted from present-day tomography models shown that mid to upper mantle hot anomalies are integral in generating IOGL. Here we assimilate plate reconstruction global convection starting 140 Ma and show sinking Tethyan slabs perturbed African Large Low Shear Velocity province generated plumes beneat...

In this article, we study the steady generalized Navier-Stokes equations in a half-space in the setting of variable exponent spaces. We first establish variable exponent spaces of Clifford-valued functions in a half-space. Then, using this operator theory together with the contraction mapping principle, we obtain the existence and uniqueness of solutions to the stationary Navier-Stokes equation...

Nowadays the GPS measurements are one of the most frequently used technique in geodesy. With this technique ellipsoidal height can be reckoned. However in the engineering practice orthometric heights (height above sea level) are used. The orthometric heights are determined by levelling. Transforming the GPS-derived ellipsoidal heights to orthometric heights it is important to know the distance ...

We consider the stationary and non-stationary Navier-Stokes equations in whole plane $\mathbb{R}^2$ exterior domain outside of large circle. The solution $v$ is handled class with $\nabla v \in L^q$ for $q \ge 2$. Since we deal case 2$, our larger sense spatial decay at infinity than that finite Dirichlet integral, i.e., $q=2$ where a number results such as asymptotic behavior solutions have be...