On the Existence and Uniqueness of Solutions for Nonlinear System Modeling Three-Dimensional Viscous Stratified Flows

Andrei Giniatoulline, Tovias Castro

Department of Mathematics, Los Andes University, Bogota, Colombia.

DOI: 10.4236/jamp.2014.27061                

Abstract

We establish the uniqueness and local existence of weak solutions for a system of partial differential equations which describes non-linear motions of viscous stratified fluid in a homogeneous gravity field. Due to the presence of the stratification equation for the density, the model and the problem are new and thus different from the classical Navier-Stokes equations.

Keywords

Partial Differential Equations, Sobolev Spaces, Fluid Dynamics, Stratified Fluid, Viscous Fluid

Conflicts of Interest

The authors declare no conflicts of interest.

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