Study of a Nonlinear System of Partial Differential Equations Associated with Stratified Fluids in Three Dimensions

Abstract

In this paper, we will show some mathematical properties for a nonlinear system of partial differential equations, which describe the dynamics of internal motions of an exponentially stratified fluid in three-dimensional space. Basically, we will study the existence and uniqueness of the weak solution for our system of partial differential equations involving the nonlinear advection term on a finite interval.

Keywords

• stratified fluids
• non-viscous fluids
• nonlinear advection term
• system of partial
• differential equations
• sobolev spaces
• galerkin method